While this is technically true, it does not appear that either guarantee the rights of citizens to speak freely, especially when the speech is objectionable. When I lament the lack of a Constitution, I lament a Constitution which permits us the same inalienable rights. Both Australia and Canada place harsh restrictions on speech.
As for enshrining rights, Canada has the Canadian Charter of Rights and Freedoms[1] which is a constitutional document that includes the freedom of expression. New Zealand has the Bill of Rights Act[2] which includes freedom of expression. As mentioned before, it's not entrenched law (though it was originally intended to be) but since most countries don't have constitutional bills of rights, this is hardly unusual.
As for Australia, I personally do think we should have a bill of rights of some kind (currently the basis of freedom of political speech is based on a High Court ruling about the Constitution's preamble which is in my view incredibly flimsy). I personally wouldn't model it on the US Constitution -- I would base it on the NZ Bill of Rights, but that's a minor detail.
However, it's simply not true to say that those countries don't have constitutions when you actually want to say that they don't have constitutional protections of certain rights (and in the case of Canada, they actually do!)
While this is technically true, it does not appear that either guarantee the rights of citizens to speak freely, especially when the speech is objectionable. When I lament the lack of a Constitution, I lament a Constitution which permits us the same inalienable rights. Both Australia and Canada place harsh restrictions on speech.