Yes, we have six states and several territories:
States: Queensland, New South Wales (NSW), Victoria, Tasmania, South Australia, Western Australia
Mainland Territories: Australian Capital Territory (ACT), Northern Territory
Both the ACT and Northern Territory have had attempts to becomes states, but failed. I'm not sure of the legal situation or complexities, but I remember the Northern Territory having a recent referendum on the subject and the attempt failed. While these two territories are really states for most practical purposes, they don't have all the legal rights of the states. It only happens rarely, but the federal government has the power to overrule territory legislation. The two times I can recall are when the Northern Territory passed voluntary euthanasia laws, and when the ACT passed same-sex civil union legislation.
We also have some non-mainland territories, but I can't remember them. The main one I know about is the Australian Antarctic Territory -- the biggest in Antarctica.