Welcome to the family Elina and Apple

.
I am in Australia Also.
Here there are many parrots you can buy as pets. But the most common are rosella's, lorikeets, Cockatoo's (major mitchells and sulphur crested) and my favorite the red tailed black cockatoo, galahs, Alexandrines, conures, Indian Ringnecks, eclectus, african greys, Karikis, cockatiels and you can find Mccaws.
Anyway I hope the following site can help you more about importing a pet bird into Australia.
http://www.deh.gov.au/biodiversity/publ ... birds.html
and/or
http://www.deh.gov.au/biodiversity/publ ... -birds.pdf
Amazons are not very common here but i have seen evidence of people with them, for example the following link shows someone in Australia with one, so I know they must be here just from that. But easy to find a breeder and buy one? I really don't think so. Unless someone else here (at this site) knows of one:-
http://zachary.avianavenue.com/WorldAmazons4.html
And a site below, of breeders in Sydney that sell among other birds, blue fronted amazon's, not sure how reputable they are, but there is a contact number etc. So it seems with a bit of hunting you could find them.
http://vanessasexoticbirds.greatnow.com/
Cheers !