Supplemental to the other answers:
David Leyonhjelm of the Liberal Democratic Party (Australia) is the most prominent voice of overt libertarianism in Australia, the way Americans would recognise it. He gets to be that by virtue of getting a Senate seat (through people confusing his party name with the Liberals, as he has cheerfully admitted).
Libertarianism is not mainstream in Australia, which rather likes Big Government. In fact, my realisation that I’m sympathetic to prioritising more individual liberties puts me out of sync with the Australian mainstream. (And in sync with groups I’d rather not be in sync with.)
Of the other parties David Caune mentions, I’d have thought (though I haven’t particularly researched it) that social conservative religiously driven parties are palaeocon, and not visibly libertarian. That includes Democratic Labour Party, Rise Up Australia, Family First, and the Shooters and Fishers Party. The populists of One Nation and the erstwhile Palmer United Party don’t count either. The Sex Party are socially liberal (including pro-euthanasia). I don’t know how libertarian they actually are, even though they are the default recipients of my protest vote.
But beyond that, as David Caune has pointed out, the Institute of Public Affairs think-tank has yielded significant influence in the Liberal party, and its rhetoric is libertarian. A recent book on the whole Abbott debacle, Battleground, was a moment when the scales fell from my eyes: explaining the ideological split within the Liberal Party, Peter van Onselen pointed out that the best way to describe the Liberal moderates was a word that never had occurred to me: libertarian.
All of a sudden, a lot about George Brandis (attorney-general) and Christopher Pyne (education minister, defence minister) made sense.