To register a .com.au or .net.au domain, you need to be able to prove that you are doing business in Australia. This usually takes the form of providing an ABN, ACN, ARBN or Australian-registered trademark.
While you can obtain a sole-trader ABN quite easily, sadly there are no options available for private individuals who are not in business to own .com.au/.net.au domains. The .com part of the domain is shorthand for "commerce" and while the generic .com domains allow anyone to register them, the .au Domain Administration (auDA) has reserved these spaces for commercial enterprises.
Similarly, to register a .org.au or asn.au domain, you need to prove that you are a not-for-profit body such as a sporting club, charity and similar.
For further information concerning .au registration policies, you can read auDA's domain name eligibility policy HERE