Yeah, nah. There was a high court ruling along the lines of implied freedom of speech, but this was, later knocked into its box by a unanimous supreme Court ruling stating there is no personal freedom of speech, implied or otherwise in our Constitution. Leaving the door open for the NZ prime minister to sue the ABC and Four Corners for defamation.
The Australian constitution is nothing like the US one, it has nothing to do with the rights or freedoms of the populace, rather it was written around the time of federation as a framework for the governance of the nation.