In LoTRO, Loremasters have several pets both combat and non-combat. You also don't have to PvP if you don't want to. If you want more info/have questions send me a private message. I can also give you a guest pass.
LoTRO (Lord of the Rings Online) is a good story driven MMO that is relaxed, fun, and has a very similar interface to WoW. If you want more info/questions about the game just send me a PM. I can also send you a guest pass.