Sometimes when travelling, there are moments when you step away from yourself, look at what you are doing and say, “How on earth did I get here?”

It was a question I found myself asking in the Mornington Peninsula while being dragged along the ocean by a rope, singing Coldplay’s “Yellow” through a snorkel. I can see why you might think I was a stubbie short of a six-pack. But I was assured by our dolphin-swimming guides that the only way to attract these intelligent mammals was to sing to them. So what better than a little bit of England’s pre-eminent rock quartet to stir the dolphins to the surface?

But the stars obviously don’t shine for them and everything they do, because I saw chuff all while I was belting out the tune. I carried on singing, in that way you do when you only know three lines and you repeat them constantly, but they were having none of it. A change of genre was necessary.

Wracking my brain for a song, the first thing that came to mind was “Hit Me Baby One More Time”, and before I knew it, I was confessing to dolphins about how my loneliness was killing me. They must admire honesty, those dolphins, as mid-way through the second verse, I looked to my left and there it was. Just two metres away, a beautiful grey dolphin was swimming right next to me.

It was so close that I could make out the texture of its skin and the scars along its smooth body. A big, beady eye was checking me out for a good 10 seconds, and then it was gone, down into the depths of the bay. I decided to call her Britney.

The Mornington Peninsula is just over an hour away from Melbourne, and is quite possibly the most stunning part of Australia you’ve never heard of. A curved expanse of land that helps create Port Philip Bay, and shelter Melbourne from the rough Bass Strait, the peninsula is an achingly beautiful place that makes you want to forget the travelling lark and settle down for a decade or so.

The Mornington Peninsula is the rich people’s playground, where monied Melburnians own summer houses and go to play at weekends, but it is also an exciting and refreshing backpacker destination. It’s the perfect place to head to if you’ve had enough of the city, a destination where you unwind so much that you’re in real danger of unravelling.

Diving in the MP is extremely popular, and for good reason. The sheltered waters of the bay offer perfect conditions for both learning and discovery. From over 60 shipwrecks and WWI submarines to a vast array of colourful sealife, no two dives are the same.

The coastline is full of little nooks and crannies to go looking around, with the famous weedy seadragons – called so because all the other sealife picks on them – a must-see. Beach life on the peninsula is one of contrasts. The inner beaches are picturesque and serene, perfect for a stroll or just unfurling a towel and reading for the day. The outer beaches have excellent surf and are perfect for beginners to learn how to ride those tubes.

I’d never surfed before and was slightly wary of going out and being dumped by the kind of wave that killed Patrick Swayze in Point Break. Not that I’m paranoid or anything. I whacked on a wet suit, and after a 20 minute briefing on the sands of Gunnamatta Beach, we were out in the water and catching waves.

Or trying at least. If you’ve never surfed before the only thing you can compare it to is trying to get out of a moving bath on a big board. The weightlessness you feel in the water goes as soon as you try to get up on the board, and you need all your strength to stand up before the wave passes you by. Then you have the small matter of balancing, steering and dismounting and you’re an expert.

Whether you’re good, bad, or just plain ugly, you’ll definitely enjoy yourself and I’ll defy you not to want to go back for more the next morning. Set against all the activity, the peninsula also has a rich and colourful history. Much is centred around Point Napean, a national park set right at the end of the headland.

Not only is it full of breathtakingly beautiful views, but it is also the place where former prime minister Harold Holt went for a swim in 1967 never to return. You can walk up to a point that gives a view of the beach he swam from, and even see the bench that world leaders sat on for the memorial service – I swear I saw “LBJ woz ‘ere” etched into the wood. Point Napean is also the sight of the first shots fired in both World War I and II.

While Europe declared war and then went off to bed, the Aussies woke up to find German ships trying to hot-foot it out of the harbour. They even fired at a Tasmanian fisherman, who after one too many Cascades, forgot to put the right friendly flags on his mast.

The big gun turrets are still in place now as a quiet and eerie monument to the protection of Melbourne, and you can take a walk around the old armaments if you so desire. You can also amaze your friends and relatives by telling them you’ve been on the thinnest road in Australia.

I didn’t catch the name of it, but I’m assured you can throw a stone from Port Phillip Bay to the Bass Straight right over the top of it. Skill. And once all the excitement is over, you can retire to the picturesque Portsea Hotel for a couple of sherberts. Overlooking Portsea marina, the big hotel was once nearly bought by rich locals who wanted to close it down, but the riff-raff are still allowed in to drink and be merry.

Mix it up with the rich oldies and the spunky youngsters as the sun goes down on another day. When I was there, the sunset was spectacular and I found myself reminiscing about the amazing day I’d just had and where Britney was now. The dolphin, not the pop star, that is.