After the 2007 Election, the Liberal Party was annihilated by a rejuvenated Labor Party led by Kevin Rudd. Liberal leader John Howard was beaten in his own seat of Bennelong. Peter Costello, who was expected to take over, refused to lead the party. Malcolm Turnbull, Tony Abbott, and Brendan Nelson have all expressed interest in the job. I don't know anything about Nelson, so I won't say anything. Tony Abbott unfortunately is a social conservative, a hard-core Catholic (aka the "mad monk") who has tried to prevent abortion pill RU486 from being available. Malcolm Turnbull, on the other hand, seems to be admired by the LDP, Australia's libertarian party:
John Quiggin is predicting the end of the Liberals. While it would certainly be interesting to see a new party form out of the ashes of the old, I don’t think that is likely. I think they will continue, but the bigger question is which direction they will take. Will they continue with Howard conservativism (Abbott, Downer), shift towards the libertarian position (Turnbull) or take the UK Tories approach of going moderate (Nelson, Bishop)? How much influence will the religious right have in the new party? I don’t know… but it will be interesting to watch.John Humphries from the CIS says the following: "Turnbull has consistently called for lower tax and was apparently a fan of my 30/30 paper. He is friends with libertarians (Peter Saunders, David Russell) who sugget [sic] to me that he is one of the good guys (relatively speaking). He also apparently agrees with gay marriage."
There seems to be some more evidence on the Internet that Turnbull is a libertarian. On his blog he says the following: "I have a little bit of the inner libertarian dog in me."
Further Reading: Liberals and the LDP