You'll find, as with a large number of country specific domains, there are restrictions in place for the registration of .au domains, primarily to protect potentially valuable domain name real estate from being scooped up by foreign organisations with no legitimate interest in the .au domain space.
For more information on eligibility, you'll want to read the auDA policy at http://www.auda.org.au/policies/auda-2002-07/ [auda.org.au]; schedule E is probably the most relevant to you and, if you feel you meet the criteria, then go for it.
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