"If you'd come here last week, none of this would've been here," our driver Abdullah says as he takes us thudding through a hotchpotch valley of rare greenery in the heart of soft-as-you-like sand dunes. "This time last week, it rained for the first time in a year and the wind blew strongly. I know where we are, but it didn't look anything like this last time I was here."

"Here" is the southern Qatari desert. It's about midday on a Friday, the first day of another Arabian weekend, and we're searching for camels – a whole caravan of them, roaming a long, long way from their Bedouin owner, who's nowhere to be seen. So far, we're out of luck, and a member of our party is starting to look pretty green behind me in the rear seat.

For the last hour and a half, we've been edging along the pointed crests of huge, dazzling, off-white dunes, snaking our way across salt flats and swerving past sporadic swathes of desert traffic – Jeeps, Hummers, Toyota Land Cruisers and open-top dune buggies, all heading out for a sand-blasted razz to start another weekend's festivities in the baking heat of the 36°C sun.

Navigation out here in the desert is closer to 'third dune on the right' at the best of times, and we're about five miles away from anything recognisable – no OS, no GPS. We've not seen anyone else for at least 25 minutes, having departed the bustling seaside basecamp for the desert some time ago, leaving behind the hordes of traditionally dressed youngsters and families bumping optimistically southward into the open country like Margate-bound revellers who've replaced their charabancs and mopeds for white, powerfully air-conditioned all-wheel-drive SUV monsters.

The stragglers in our convoy have turned off for a camel-free route back to the comfort of the beach camp, leaving us to slug it out with the sand, the potholes and the guys with the humps, wherever they are. By now, slightly frustrated that the camels aren't in their usual spot, Abdullah is operating an inward spiral search technique that's more akin to a TV cop drama than a casual afternoon jaunt; we're heading into the southernmost reaches of this oil-rich peninsula nation, which pokes out 99 miles north of Saudi Arabia into the Arabian Gulf.

Families bump their way southward into the open country like Margate-bound revellers who've replaced charabancs for all-wheel-drive SUV monsters

But it's not just the sands that have blown change in Qatar – this is a place where things become less and less recognisable year-on-year. It's not just new restaurants, hotels and shopping complexes that are springing out of the desert to help sate the ever-more burgeoning trade for stopovers, short luxury breaks and business trips – there are entire new towns, cities and metro lines slowly starting to be carved out of the sand, too.

"When I was a child," Abdullah tells me, "my father used to bring me down to the sea and I'd play on the beach or swim by the Sheraton Hotel. It'd be me, the hotel and then the desert stretching out beyond it, all the way to the horizon. "Today," he continues, "we have 150 skyscrapers in the country, but by the World Cup in five years, we'll have nearer 300."

Google the Qatari capital of Doha in the early 1980s and you'll see just what Abdullah described: the pyramid-form Sheraton Hotel appearing out of the sand like the tip of a gigantic, part-buried ocean liner, the yellow desert rearing back into the distance behind it, met by a single slender road.

Today, however, the Sheraton shimmers on the built-up waterfront with an original-trilogy Star Wars kind of anachronism about it, the marble-adorned foyer and interior looking like a termite mound reimagined by James Dyson. It's supremely luxurious, of course, but so are most of its neighbours in this, the world's most wealthy country. So why is it the Sheraton that remains the centrepiece of the lustrous Corniche?

The answer: age – or at least that's what I hear in the reverence every local adopts when they speak of it, or see in the faces of the crowds of people at huge events like the Qatar International Food Festival, which was moved to its lawns this earlier year. Even though it's only 38 years old – a slip of a lad in comparison to London's oldest hotel, the 180-year-old Brown's Hotel in Mayfair – this pyramid, not unlike those in Giza, Egypt, would appear to be a relic to the start of a special new era for the people of Doha: one of prosperity and glamour.

It's far more than this 40-year history that gives Qatar its kicks, though. This is a country that values a deeper, much longer-ingrained culture, too. You can see it in the thousands of people that make their way to Souq Waqif on a Friday night and the crowds that flock through the doors of the Museum of Islamic Art on a Saturday morning.

I go to both, the former a brushed-up bazaar of restaurants and vendors that's full of everyone from somnambulant tourists plodding through the first few hours of a stopover visit, to purposefully moving families inspecting wares as varied as spices and falcons (yes, falcons) in narrow but immaculately clean alleyways.

The latter, meanwhile, is a five-floor walk-through of Islamic art, stretching back across 1,400 years and three continents. Glazed bowls from India, tilework from Iran, enamel-painted glassware from Jordan, surprisingly accurate trading maps of the Mediterranean from over 600 years ago – each darkened room is a step further into the technicolour inner sanctum of Muslim history, adding another layer and level of nuance to what it is to be Qatari today.

Where to stay in Doha, Qatar

The Ritz-Carlton Doha

Refurbished this year, this hotel now boasts a top-floor restaurant with live jazz and a marina-view games room that's also Qatar's only pub.
B&B from £155. ritzcarlton.com

Sharq Village & Spa

Private beach? Traditional lodgings? Infinity pool? Yup, this resort is pretty unique. Eat at Parisa – one of the most authentic Arabian restaurants in Qatar.
B&B from £210. ritzcarlton.com/sharqvillage

Four Seasons Doha

As if supreme luxury wasn't enough, the Four Seasons has a quayside Nobu with an outdoor seating area looking back across the Doha skyline.
B&B from £240. fourseasons.com/doha

Shangri-La Hotel Doha

Chill in this hotel's secluded seventh-floor garden oasis right in the heart of the city. It's complete with a curved outdoor pool and swim-up bar, natch.
B&B from £150. shangri-la.com/doha

Marsa Malaz Kempinski

A jewel in the Pearl, a luxurious man-made island in the north of Doha, this palatial hotel is full of top restaurants like Levant-inspired Al Sufra.
B&B from £510. kempinski.com

But one thing in particular catches my eye: a burnished war mask, immaculately gilded and originally found in the Eastern Caucasus in the 15th century, the discard of some long-departed war lord battling it out on the frontiers of the old Islamic world.

A couple of hours later, it's sitting on my dressing table in the Ritz-Carlton hotel. Not the real mask, I should add, but a gold leaf-covered chocolate version, made by the hotel's in-house chocolatier and given as a gift when I checked in. And it's this that really showcases what modern Qatar is about: Luxury, definitely. Heritage, undoubtedly. Audacity, quite possibly. But most certainly, generosity.

"People here buy gold Bugattis just because they can," my guide Jamal says, "but the same people will load up your plate with more food than you could ever eat, because that's what Qatari hospitality is like. If you're visiting us, we want you to be at home."

Even though only a little more than 12% of the country's 2.3 million population is natural-born Qatari, this lavish generosity insinuates itself into all aspects of the country's culture, from the food served to you at dinner, to the Emir himself, who – as Jamal jokes – the nation hopes is entertaining the notion of buying Manchester United, if only to up the stakes a little against City in the Manchester derby.

But beyond the outward-looking desire to dazzle, Abdullah has a different story to tell. Dropping me back at my hotel after dinner, he says that he's heading home: "I need to call my father. He's asked if I need any help with my work. I said no. He's retired – he needs to look after the family home; I need to show visitors our country."

Tomorrow, he says, they'll gather for a meal – his parents, his brothers and sisters, their partners and all of their children – many of whom all share a large housing complex built on money granted by the state at marriage. More than 30 under a single roof, they'll relax (as much as they can given the shrieking of so many children, he says), eat and catch up on what's happened in the week since they last sat down together. For every new building that challenges the height of the last, every plate of food that tests the notches in my belt, and every aspiration that looks to go further, glitzier, newer or better, there is also family: equally voluminous, equally chaotic as the growing sprawl of Doha, but equally a great source of pride.

Back in the desert, we find the camels. Abdullah, clearly well-versed in the art of camel calling, punctuates the calm desert breeze with a sharp "Ay, ay, ay!" at the caravan until one of them approaches, gently lowering his head to our open window, so close we can smell his breath and feel the moistness of his slobber.

Satisfied, we're off – one last stop before we reach the Sealine Beach Camp for tabbouleh, fattoush and kofte, though: the Inland Sea. After another purposeful 25-minute drive down an incredibly flat desert highway channeled through the dunes by a combination of wind and years of invisible desert traffic, we pull up about 30 yards short of a deep shelf in the sand.

"Hop out," Abdullah says, stepping confidently down onto the sand and into flip-flops. "Take five minutes – you might want to take some pictures." He's not wrong. From here, we're in spitting distance of Saudi Arabia. A heel-skidding sprint down a monster dune and we could be swimming across the border and taking a dip in the Inland Sea – the 180km² saltwater creek fed by a 10km-long tidal channel from the Arabian Gulf. This is one of the few too-good-to-be-true sights in this small country that hasn't been painstakingly crafted by man and bankrolled by oil.

Lusail, a new city directly to the north of Doha's current sprawl, will be a wonder of the other kind. Touted to house another 260,000 people as well as marinas, island resorts, luxury shopping and the Lusail Iconic Stadium – home to the 2022 World Cup final – it's a prime example of the Qatari approach to construction. Nothing is more important than ambition.

I'm watching it come up through the window of the 23rd-floor club lounge at the top of the Ritz-Carlton hotel. A personal chef enters the room, clocking on for the morning shift, offering me pastries, eggs benedict, salad with labneh. The sun rises over the Gulf, expat runners heading out along the Pearl while a bleary-eyed Abdullah sits in the lobby drinking a Red Bull. The Doha Expressway yawns back into frenetic business after a brief, four-hour slumber and somewhere beyond the early morning mist, ground is broken on the stadium which will play host to the World Cup final in five years' time. There's still a lot more to come.

Book transfers, tours and activities with Falcon Tours. falcontoursqatar.com; Qatar Airways offers direct daily flights to Doha. qatarairways.com; For more information on holidays to Qatar, go to visitqatar.qa