In fact there's no where on the planet where I don't have an accent, and I'm old enough that this will always be true. I am well and truly screwed.
Reason is simply that when I was a kid, the house next door - the only house next door, this being rural Norway - was purchased by a family from Aberdeen, who'd decided to move to Norway to try something new.
If I wanted to play with their kids, I'd better learn some English fast - and the only speakers around were the Scottish kids next door.
Incidentally, I now go to Aberdeen for work on a regular basis, and the locals never fail to ask how long I've been living there, seeing as I've started to pick up their accent and all...
I've lost most of that except for a residual tendency to say eye-ther (either) and tomahto (tomato), which my Strine wife smirks at.
It's a mistake to think that there is a single Australian accent.
I live in central Melbourne, and most people I meet have an accent very similar to a Kiwi accent, close enough that after only a year since I came from NZ, most people think I'm an Aussie. The accent has been easy to pick up, just say 'feesh and cheeps' and use a high rising terminal (like you're asking a question), and you're good to go.
However, go to the outer suburbs, or rural Australia, or up the coast to NSW or QLD, and you get a whole array of different accents. You've got the ocker accents, the wog accent, the aboriginals have their own accent.