No rights written into basic law? No rights.
To eliminate the Englishman's right to arms, the elite simply stopped talking about it, and the courts refused to acknowledge it after WWI.
The Australian Constitution was written in 1900 and ratified on 1 January, 1901.
Australia is a strongly federal system. The individual states have stronger powers, in many ways, than American states.
When the Australian Constitution was written, a bill of rights was not included. Instead, the Australians relied on the traditions of the rights of Englishmen.
Consequently, individual rights to arms, to freedom of speech, to requiring warrants for search and seizure, all depend on the traditions of the courts and precedent.
Some protections are strong, some not so much.
The right to arms is almost completely gone,it lingers only in that the courts have ruled the police must follow procedures when granting firearms permits. Thus the police are not able to simply deny a permit. They are, however, granted wide latitude. If you do not have all your i's dotted and t's crossed, you very likely will not get a permit.
The requirements to prove you have a legitimate "need" for a firearm are significant, but they can be met.
Self defense is not considered a "need" to own a gun in Australia, since 1997.
Warrants to search homes seem more rigorously required than in the United States.