That time in Exmouth, Western Australia, when an emu was clearly fascinated by how effortlessly a human can move around.

I really recommend Western Australia above any other part of Australia if you want to see the version of Australia that may fit your stereotypical outback idea best. Most of it is wilderness, and even when you go into the towns you'll see all kinds of lovely creatures. Not all of them are venomous or otherwise dangerous, either.