how do you get rid of rats and mice without killing your dog?
Answers:
Depending on where you sit on the PETA scale (from "I really want to get rid of them but I don't want them to suffer" to "I want them dead and I don't care whether they suffer"), you can use either box traps (available from humane societies and hardware stores) or glue traps (if you don't care about the little buggers).
Other answers: