While it is true that the Democrats have more consistently supported treaties and Bill of Rights legislation, it's not true that other parties oppose human rights protections. Some in both major parties don't like particular human rights (for instance, some in the Liberal party aren't real keen on the rights of homosexuals, while some in the Labor side of politics don't mind squashing free speech if it expresses racist or sexist views), but, on the whole, Australia has signed most of the human rights treaties out there under one or other major party. As far as Bills of Rights, that got knocked down in a referendum the last time Labor tried it IIRC, and they're not keen to repeat the experience, and many in their party and most of the Liberal Party take the view that human rights are better protected by a democratically-elected parliament and an independent judiciary than constitutional amendments that may have ramifications far beyond what the framers or voters intended when they were imposed and may turn out to be counterproductive to more contemporary interpretations of human rights (for instance, consider the US first amendment, which many view as the right to have a murder rate many times higher than any other western society). I'm not necessarily agreeing with this viewpoint, but claiming that the major parties are anti-human rights is bollocks (though their recent efforts with regards to asylum-seekers might themselves deserve a bollocking IMHO) -- Robert Merkel
The last attempt at an Australian Bill of Rights was not knocked over by the people as you suggest, it was knocked over by the Liberal party, who first insisted on taking all the good bits out of it before the referendum was held, and then campaigned against it very strongly.
The most serious human rights problems in Australia are indefinite detention without trial, seizure of property without a warrant and with no possibility of judicial review, and the lack of any mechanism to investigate or punish police and other government officials when they murder law abiding citizens. Some sort of freedom of speech would also be nice. Both Labor and Liberal have systematically opposed any attempt to do something about this at both state and federal levels for the last ten years, and less systematically before that.