For a moment, I fear I’ve had too much bubbly. But a fellow passenger sees the beast too — there’s a camel in the Australian Outback.

We’re enjoying canapés and champagne on one of the greatest rail journeys in the world, so admittedly, we’re a little distracted. But if I’d paid more attention to our locomotive’s name, I probably wouldn’t have been so surprised by the dromedary in the desert.

Our train, the Ghan, which is taking us right through the heart of Australia, was named after the Afghan camel drivers who helped open up this remote continent. The epic 3,000 kilometre journey runs from Darwin in the north to Adelaide in the south.

In the 1800s, they carried sleepers and supplies for workers building the railway. But when the original line, from Adelaide to Alice Springs, was completed in 1929, the men were out of a job, and set their animals free in the desert. It led to around a million wild camels in Australia.

As for the railway, it was rebuilt and re-routed several times. But it wasn’t until 2004 that it was extended right across the continent, allowing people to travel all the way from the Northern Territory to Southern Australia.

The journey typically takes three days. But now there’s a four-day Ghan Expedition Trip, in which the train stops for various excursions en route; I was lucky enough to be one of the first to try it.

We leave the steamy heat and lush vegetation of tropical Darwin, and are soon rolling through dense forest, towards Katherine, 300 km south.

Our first stop is Nitmiluk National Park, the traditional land of the Jawoyn people. There’s a choice of excursions (all included in the price) plus a couple of optional upgrades.

While fellow passengers go for a cruise along the Katherine River, a small group of us take a scenic flight over the area’s sandstone gorges.

We soar over an arid landscape, sliced by the glittering river. The Jawoyn believe it was formed when a cave bat killed Nabilil, a crocodile, and in so doing, pierced the water bag he was carrying with his spear. I spot plenty of waterfalls, spilling over the splintered rockface; there’s even the odd crocodile and water buffalo.

Our pilot reveals that somewhere in the 300,000 hectares below, 40,000-year-old petroglyphs have been discovered in a cave. Apparently Oprah has seen them and he hasn’t.

“I’m a ranger here! How can they not tell me where they are!” he says with mock indignation, before taking us down to a picnic of cheese and champagne on the airfield.

The Ghan rolls on towards Tennant Creek, home to cattle stations the size of Belgium. We travel at around 85kph: our 30 carriages, led by a red, liveried locomotive, weave through the land like a sinuous snake.

I sit in the Explorer Lounge, surrounded by books and board games. It has a gloriously old-fashioned feel, with burgundy leather chairs and sand-coloured tables that blend into the surrounding desert. Through its large windows, I spy the odd dirt road or wind-powered water pump, as clouds, like UFOs with grey underbellies, steer through an expanse of sky.

Robyn, the restaurant manager, has travelled up and down Australia for the past nine years; I ask if she ever gets bored. “Never,” she replies, “because I always seem to glance out of the window at different times in the journey.”

The Ghan’s meals reflect the regions we travel through; in the north, we dine on saltwater barramundi, goldband snapper, kangaroo and crocodile. Further south, there’s salmon from smokehouses in the Adelaide Hills and cheeses from local producers, including an award-winning Woodside goats cheese and an Onkaparinga blue.

All food and most drinks are included, and there are some beautiful red wines from the Barossa Valley.

I’m staying in Gold Class (there’s also Premium), in a cabin with two bunks and a shower. I sleep with the blind up, to see the sunrise, and as we pull into Alice Springs, the rocks of the Red Centre glow russet and gold.

We spend a full day in Alice, visiting the Flying Doctor Service Museum, Anzac Hill and a reptile centre, where the owner, Rex Neindorf, is so entertaining, I almost forget there are Tasmanian Devils and snakes to see too.

But my favourite stop is the old Telegraph Station, just out of town. In a handful of 19th century buildings, overlooking the waterhole from which Alice Springs took its name and shaded by gum trees, I meet enthusiasts from the country’s Morse Code Society.

They invite me to send a telegram down the line which once linked London with Australia. Although most of the original eucalyptus poles were eaten by termites, one is still standing. I chat to Ron and his pal, John, who were telegraph boys in Alice in the ’50s as John speedily taps out my message.

That evening, we have an Outback barbecue in an old quarry in the East MacDonnell Ranges. Tea is brewed in large billycans and there’s a sing-a-long round the camp fire, with camel rides for the adventurous before the train presses on through the night.

On our third day, we pull up at Manguri where the Ghan, a staggering half a mile long, comes to a halt on a vast, gravel plain. There’s no station or platform, so cabin attendants run up and down the carriages, to line up steps with the doors.

Coaches take us to Coober Pedy, a settlement 40 km away, where locals live underground to escape the searing heat. The aboriginal people gave the place its name; it translates as “white man’s burrows”.

The township grew up round opal mining; we hear tales of men who made (and lost) a fortune while Robyn organises lunch in an underground mine, complete with hard hats.

The next morning, the bleached soil gives way to the green pastoral land of South Australia. There are farm silos and wheat fields and the endless Flinders Range, mountains rolling up and down in the distance.

As we draw into Adelaide, the Ghan gives a toot and we come to a final stop. I fear I will miss the train’s odd little rattles and gentle rhythmic sway. Dropping onto the platform, I know my trip’s been very different from those first cameleers who forged a route south through this continent, but I arrive with the same sense of elation.