I've done the same trip two years ago when LCA was in Canberra, and would definitely recommend doing the car option. You should plan for at least one week to go to Melbourne by car, and if you have another week, I can recommend going on to Adelaide via the great ocean road.
I'd strongly suggest doing the Great Ocean road if time permits. Beautiful coastline. -- Michael Davies "Do what you think is interesting, do somthing that michael@msdavies.net you think is fun and worthwhile, because otherwise http://michaeldavies.org you won't do it well anyway." -- Brian Kernighan