You must provide an active registered Australian entity ID to register any .au domain name.
An ABN is the most common form of ID to register .com.au, .net.au, .org.au or .asn.au domains. However an ACN or a registered trademark or an incorporated association ID can also be used.
To register a .org.au or .asn.au the organisation must be a non-commercial organisation registered as a charity or non-profit organisation or an incorporated association, otherwise the registration will be rejected by the Registrar.
A complete detailed list of eligibility requirements for each domain type can be found on the domain authority website auda.org.au.