So I'm working on the Cat Lady achievement and in order to get my last cat I'm doing Raiding with leashes ( More rad pets never hurt anyone). I've done the raids twice each and haven't had a single pet drop. Bought a bunch at the ah, but I still have 3 left. Can you really only kill each boss once a week? This is gonna take forever isn't it?
The lock out is per character so if you've got multiple high level characters you can run each of the raids once per character per week. Otherwise, yes it can take a while if you don't want to or can't buy everything in the AH.
Lockouts are once a week per toon, though I'd also suggest bribing any buddies you might have into helping you farm as well, just to increase the chances (maybe you can offer to pay them a bit of gold, or offer to help them with whatever they might need in return).