I'm at a hotel right now that allows pets on the shop, but don't think I would take a pet even with that option.
There are extra component to the shop if you do take the pet that others do not have to perform, and having done it once before, I can say that it's just not worth the extra hassle. I called twice yesterday to get my room made up and was out of the room most of the day just waiting for housekeeping to service the room. Having to deal with that kind of hassle AND my pet would make the shop difficult.