SCoates: Actually technically speaking it's "Australian". Aussie, also written Ozzie, is a nick-name, thus it is pronounced the way we want it to be.
The name Australia comes from the Latin for southern, 'australis' (aw-stray-liss), so English people (who named the country) tend to pronounce it awwstralia. We're much too lazy for that, we like to pronounce it osstralia. Much easier!
So you see, if we were going by historical roots, we'd be going around calling ourselves "Awwsies". But that's even sillier than Ahsie (which sounds rather like an insult if you know the Australian accent)
Ha ha, I'm right, you're wrong.