Registrations for .au domains are regulated by auDA (the au Domain Administrator).
In general, to register a .au domain name you must meet the eligibility requirements set down by the .au Policy
It is your responsibility to ensure you meet the eligibility requirements before submitting an application for a domain name. If you do not meet the requirements, your application may fail. Even if you successfully register a domain, if it is later discovered that you do not meet the requirements, or your circumstances change and you no longer meet the requirements, you may face the prospect of losing your licence to the domain.
The current Domain Name Eligibility and Allocation Policy is available at:
http://www.auda.org.au/policies/auda-2005-01
A complete list of published policies is available at the auDA website:
http://www.auda.org.au/policies/current-policies