What happens if you want to call your band a name in Australia, but you find out that there's a (non-famous) band in England with the same name (including a website and myspace page). Can you still call yourself the same name and see who makes it big first?
No. Not at all.
Although The Australian Doors or Abbaration are acceptable as alternatives to the proper names, as an example.
So what you're saying is that you can't take a name that is already taken, even if that band isn't famous?

I've got CDs by both the 60s UK Nirvana & those guys from Seattle, & by the UK & US Kaleidoscope. Then there were the British (as in Cliff Richard & The) & US Drifters. The British ones changed their name to the Shadows.
You really need to choose a distinctive & (preferably) several word name.
I've got a great idea for a name: but someone else is already using it. :)
But they're not famous and they might break up next week.

Just add and umlaut over one of the vowels. Although that means you're pretty much committed to being a speed metal band.
Depending on how original the name is e.g. The Doors vs. Bare Naked Ladies combined with the fact that the other band is in the U.K. and you're in Oz I would think you really don't have an issue. If you're really concerned you need to talk to a copy right lawyer who knows international law and go with what he directs you to do.