I hope for the sake of everybody currently living in Australia that your description of their mice was hyperbolic. That sounds terrifying! We have found mice easy to trap (and we have many, many of them), but the rats are a different story. We have tried every kind of trap and poison, and the only thing that has worked is the dog. We got her convinced it was her job to catch them and she has been doing it regularly. Luckily, the rats are not in the house. They live under the chicken coop. I don't really mind the mice as long as they're not in the kitchen.
Ha ha... Yes perhaps it was a little bit overblown! Rats... I don't know what to do if we had those! It looks like you know how to keep them at bay, so I'll check in with you if things get out of hand... But I think rats are off the radar at the moment!
My husband attached a dead rat to a fishing line and threw the rat out into the yard and reeled it in to make the dogs chase it. It was a little gross but super funny and sure got the message across!
Hmm.. I don't have a dog, but I have two children... Maybe I'll try it out!