It's not actually just an Australian term for a hurricane. It's a special type which occurs in the outback, when a swirl of wind picks up wind or sand and spins it around tornado-like. This is very small scale and lasts from about 5 seconds to about 10 minutes.
A willy-willy is like a wet willy, but instead of putting your finger in your mouth first, you put it in your own ear and wiggle it around first to get a nice coating of wax. Then you insert it into someone else's ear.