I decided to camp the night at Thredbo Diggings on Andrew T's suggestion. The road from Canberra to Cooma was quite busy, though from Cooma to the diggings was quite peaceful. It cost $16 to enter the Kosciuszko National Park, and the camping was free. The campground is quite pretty and popular. The ducks are quite insistent about being fed and the kangaroos are quite curious too. I didn't see any platypus or go for a walk as it was too wet and cold, and I didn't bring the right shoes.