Anything, really. There is no relevant degree as such, but some would argue that a law degree is now a necessity in order for one to exhibit clarity of expression when in Parliament. However, that's a load of crap, as far as I'm concerned. It's the person, not the degree, that matters in this regard, and it isn't as though a law degree is the only one that allows a person to develop what many would consider to be the requisite skills for a life in Canberra (or a state capital, too). What's important is making your presence known and being of sound mind (and personal and profressional 'integrity', whatever that may be).
Edit: A degree isn't really a necessity to enter parliament, rather it's your position within the local branch of the party and your standing within the local area come an election. Beyond that, it's your performance in parliamentary committees and your ability to carry an argument and your clarity of expression that should determine whether you scale the heights and reach the Cabinet or not (at the moment, though, it's more a case of who you know and whether you are willing to sacrifice your personal position for a promotion (Ruddock, anyone?)). A degree would be of great assistance in developing the skills required to make an impression in the field of policy, but it isn't a necessity.