Thanks a lot for all the info, much appreciated. For snowboarding, I know my timeframe wouldn't be the best. However, I had a quick look a while ago and I remember that a two-way ticket from Melbourne to Queenstown around september (example) would be about 200-250$. So it would be a really nice option to break the summer a bit by spending a week snowboarding, than back to Aus, and visit NZ probably during the summer.
Renting/buying a car, for Aus and NZ as well, is something I'm still debating and will probably take my final decision there. Cost wise, if I am wise in my moves, it really wouldn't cost more than using trains/planes/busses and sleeping in hostels since you can easily carry full camping gear in a car, so that offsets some sleeping cost. You can also give rides and do some legs with random people you meet along, bringing it cheaper again.
I just have a hard time finding factual non-contradictory information about what to expect in terms of paperwork/insurances etc as a foreigner.
Also, I fully expect that left side driving thing to bring a close call or two