Roger Federer started it when he took a selfie with a small, grinning marsupial and posted it to his 31 million social media followers. Then fellow tennis star Rafael Nadal did the same thing last year and suddenly the world went bonkers for quokkas. But taking a quokka selfie is easier said than done. First, you have to find a biddable quokka. These round furballs, about the size of an over-fed domestic cat, roam freely on Rottnest Island, a protected nature reserve off the coast of Perth, Western Australia. With no natural predators on the island, they are endearingly tame. But not all of them got the memo on social-media etiquette. The first one I sidled up to looked at me oddly, then wandered off. A second was too distracted by his friends to look at the camera. But the third quokka turned out to be the Kate Moss of the marsupial world, smiling broadly as I lay on the ground next to her, snapping away on my iPhone. She smiled, she gurned, she turned her head from left to right, yet never once lost eye-contact with the camera. What a star! Quokkas, which are native to Rottnest, have managed to put an island that no one outside Australia had ever heard of firmly on the tourist trail. But when you’re there, you wonder why it took so long. ‘Rotto’, as the locals call it, has everything you could possibly want in a holiday spot, crunched into just seven square miles of coastal bushland. No cars are allowed on the island, so everyone bombs around on pushbikes and e-bikes, stopping to spot examples of the 50 native bird species or go for a swim at one of the 63 beaches, all so ridiculously pretty they look as if they have been lifted from a Disney version of Treasure Island. As Rafael Nadal demonstrated when he emerged dripping from the sea to millions of Instagram likes, this water is something else. Fringed by coral reefs and teeming with tropical fish, it is the Indian Ocean blue of a Curacao cocktail. Yet it was Rottnest’s grim past as a prison island for aboriginal men in the 1840s and later as an internment camp during both world wars that kept it in the dark for so many years. It wasn’t until after World War II, when basic bungalow accommodation was built for local families, that it began its reinvention as a holiday island. Now, with a new memorial recognising the thousands of aboriginal lives lost there, Rottnest is putting its dark days behind it to emerge as a destination fit for the 800,000 international tourists who spill off the ferries every year. As there is very little overnight accommodation on Rottnest, most tourists take the 25-minute ferry from Fremantle, near Perth, there and back in a day. But I managed to grab a bed at newly opened Discovery Rottnest Island, a cluster of posh eco-tents with proper beds, ensuite bathrooms, a swimming pool and on-site restaurant. Oh, and a quokka waiting for you with a smile on your private sundeck each morning. With this influx of international visitors comes a new swathe of what the tourist industry likes to call ‘experiences’. You can walk around the island with a botanist or spend a glorious day, as I did, on a Wild Seafood Experience Cruise, which pretty much does what it says on the tin. You jump aboard a boat that takes you around the island, stopping to haul in lobsters, which are barbecued on board and served with mountains of coconut rice, oysters, barramundi and a bottomless supply of Margaret River chardonnay. What’s also appealing about this insane Aussie summer decadence is that it is now only 16 hours away from wintery Britain. I hopped on the direct Qantas London-to-Perth flight in sleet and hopped off in dazzling 34c sunshine. While Perth used to be known as a pit-stop on your way to somewhere else, it has morphed into the sort of action-packed destination that could eat up your entire holiday allowance. After landing, Perth’s city centre is definitely worthy of a night or two. Book a walking tour around the city to discover the secret laneways covered in wild and beautiful street art, whisky speakeasies hidden in basements and the tiny restaurant you would never normally find which serves the best pizza in town. The West Australian Museum has just reopened after a £200 million refurbishment and features a blue whale skeleton the size of a school bus. Jump in a taxi and head to Perth’s grandest city beach, Cottesloe, where you can swim in the surf, sunbathe on the lawns, then walk up to The Shorehouse for a lunch of blue swimmer crab and prawn linguine. The most direct ferry to Rottnest leaves from Fremantle, a port city just south of Perth, but this pretty cluster of restored Federation houses and shops is a destination in itself. I stayed at one of the beautifully renovated old boozers, The National Hotel, with wraparound wrought-iron verandahs, where you can sip a gin cocktail on the roof terrace rather than sink a Foster’s on a sawdust floor. With Australia set to reopen its borders in mid-2022, it’s about time the Aussies shared this little gem with sun-starved Brits. But get there quick before the quokkas break the internet again.