This is a male koala a.k.a. "drop bear" painted from memory. I saw him on a bush walk in Katoomba recently, about 50 metres ahead of me on the track, eating his last kill. I didn't really see what his prey was, but I've painted a magpie in there as an educated guess. Obviously I didn't try to get a closer look!
P.S. If this doesn't gel with your "cute and cuddly" idea of koalas, think again. While female koalas and their joeys (young koalas) are docile enough to be held like teddy bears when you go to the zoo, the male koalas are kept in separate enclosures, both for the safety of the female and young koalas, and also the safety of the general public.
If you ever encounter koalas in the bush (wild), you will know a male by the blood staining his chest. Make sure you check the trees above you for drop bears, so you don't unwittingly pass underneath one, as they are known to drop down on their prey from their high hiding spots. While not necessarily lethal, you wouldn't want one of these little buggers ripping your face off.