Completely by chance, I happened to find a $2 shop today in Lane Cove today that sells just what I have been looking for - a pack of small, clip-on furry animals. A dozen for five bucks.
Finding them just took a bit of perseverance, and a bit of luck. I was actually searching for a cake rack (which I failed to find). I'm going to use four furry animals per pack until I run out of them. Or the kids find them.