We have possums too. From the "Brush Tail" as big as a small\medium dog, the "Ring Tail" the size of a large cat, to the tiny "Sugar Glider" not much bigger than a mouse. The bigger possums have got some attitude, pretty much endemic all over, and the Sugar Glider is a rain forest dweller. All are vegetarian, eating fruits and nectars. Most are quite tasty. Oops did I say that? Must be the Hillbilly coming out again.
For the best info on our native critters,
http://www.austmus.gov.au/factsheets/
the Australian Museum web site fact sheet page. There's lots.