Website addresses ending in .au are for a person or organisation that has an Australian connection and can only be registered to an Australian. To have an au domain, you must have either an exact match or close and substantial connection to the domain name. Further information about eligibility is detailed on the www.auda.org.au website.
The assigning of domains to match the rules is overseen by a regulatory body called the auDA (.au Domain Administration), this body is responsible for the .au registry and all domains are bought through a registrar. auDA operates with the endorsement of the Australian Government and delegated authority of ICANN, the Internet Corporation for Assigned Names and Numbers.