OP- What area are you from? Australia has a huge variety of scenery, wildlife, and cultures. You probably want to see things that are as different as possible from home. What are your and GF's interests?

One unique though touristy suggestion is the Penguin Parade at Phillip Island, about a 2h drive from Melbourne. There are many organized tours there as well.

We went to MEL, SYD, Uluru, and Cairns (Barrier Reef) in July. The Reef was the highlight of our trip and there are also amazing rainforests surrounding Cairns. As pointed out however, January will be the hot and rainy season there; at Uluru it will just be crazy hot (40-50c).

Also, I assume you meant Jan 10 in the title of your post, not 09? (Better hurry if you meant 09!)