I think I’ve seen a sign outside the Orlando Vista Hotel (which is a good neighbor hotel and within walking distance to DTD) that says pets welcome. You could call an ask. We’ve stayed there before when we were looking for homes in the area and it’s a fantastic place ~ beautifully themed and colorful and the staff is amazing.
I don’t know of any other places off-hand. I’m sure you can find the info on the hotels’ websites or call them directly. I do know that there are several day kennels on Disney property. You can even have a Photopass session with your pet at some of them!