Under the Australian Courts Act 1828 which provides that all laws and statutes in force in England at the date of the enactment of the legislation shall be applied in the courts of New South Wales and Van Diemen's Land (Tasmania) so far as they are applicable (and which includes Victoria and Queensland), and the Statute of Westminster 1931 which provides a logical end to future British law applying, the Bill of Rights Act 1689 applies in Australia.
Admittedly the Bill of Rights Act only explicitly spells out that: the freedom of speech and debates or proceedings in Parliament ought not to be impeached or questioned in any court or place out of Parliament, it does reinforce that the right exists at law.
Consequently the Right to Free Speech exists at Common Law and this was given with a few caveats as defined in James vs Commonwealth of Australia 1936:
"'Free' in itself is vague and indeterminate. It must take its colour from the context. Compare, for instance, its use in free speech, free love, free dinner and free trade. Free speech does not mean free speech; it means speech hedged in by all the laws against defamation, blasphemy, sedition and so forth; it means freedom governed by law."
[James vs Commonwealth of Australia 1936 (2) AER 1449 at 1473 PC]
The right doesn't need to be spelled out in the positive because it already exists in Common Law and expressed in the negative - we have a right to say anything that is not prohibited.
The idea that there needs to be an explicit statement is nonsense.