Domain name registration is independent and unrelated to your business name registration. There is no automatic right to register words in your business name as your domain name.
To register a .com.au or .net.au domain name, you must be a commercial entity and possess either an ACN or ABN.
Further eligibility and allocation rules apply to the various second level domains (asn.au / com.au / net.au / id.au / org.au / info.au / conf.au)