Obviously there are rascist people, and even groups, in Australia, but I don't think it's moreso than in any other country.
Talking to a couple European/Asian/Islamic immigrants, the general experience seems to be that seeking employment/education here is easier than in say, America, and equal to say Canada.
We do, however, culturally have a sense of humour whereby we make fun of each other almost as a sign of affection. So we do have disciminatory jokes that go around... but then these are generally aimed at everyone, often include Anglo-Australia and aren't only centered around race. (Think Chasers humour).
I'm about as Caucasian as it gets, so can't say my life has been overrun with discrimination, but in my travels I've also witnessed it working both ways. (I.e. against Caucasians/Asians in Middle Eastern countries).
Universally though, people seem to be pretty not phased by race.
Hmm, I guess I'm trying to say you can grab at incidents in a country and write an article on how racist that country is... but all it does is exclude the 99% of the time when that doesn't happen, and it's something you could apply to anywhere.