Most, if not all states, require a minimum of 12 months post qualification work experience, so you won't be able to go straight from uni.

Just to summarise the process to work in Aus you need to:

1) get your degree approved by the APA (you can do this as soon as you graduate)
2) Apply for the written exam....once you have applied you can work on either a temporary basis for 3 months in each job you do without actually having to sit any exams
3) if you want to work for more than 3 months in any 1 place you'll need to sit the written and the practical exams

each state in Aus has a different board with different requirements, so you'll need to check thier websites to clarify.