Then why are the petting zoos in Australia not called patting zoos? Are you aware that dictionaries often have more than one meaning per word? The proper term is petting. Patting is a completely different motion. Beautiful kitty!
I see several official Australian zoo websites that specifically mention a petting zoo. So no. You can't tell me petting is incorrect or that there are not petting zoos in AU, when their official sites say otherwise.