Hi there Stephen,
The answer is Yes and No! I will explain.....Unless they are service animals they are not allowed at any of the Theme Parks, Water Parks, Transportation Buses, Downtown Disney or any of the Walt Disney World Resorts/Areas. There is one exception to the rule and that applies to Fort Wilderness Campground. If you are asking if you can keep your dogs with you at your campsite, Fort Wilderness does have 3 loops (I believe)where they will allow you to keep your dogs (but they must be contained to this area and be well cleaned up after!).
I don't think this includes the Cabins for rent, only your own trailer. There is also a
kennel located here at the campground,(as well as other kennel locations throughout the parks) where we have kept our dog in the past and have been very happy with the quality of care he received from the staff as well as the frequent walks we could take him on, we were still able to see him every day and fuss him lots!
The best advice I can give you for more information, would be to call their Guest Information at
(407) 939-6244. They will be able to answer all of your questions and start you on the right track to have you enjoy your vacation with your lovely small dogs/family members!
Have a magical day,
Brigitta