We stayed at the Sheraton Safari a few years back and they allowed pets. However, I didn't leave her there when we went to the parks. My son lives in Orlando and works at Disney, so I left her at his apartment. They do have kennels at the parks..but I have heard bad stories...I wouldn't leave my pet there.
Now when we go down we always rent a house...it is usually cheaper than a hotel believe it or not and there are a lot of pet friendly homes included. Here is the link for the homes. The rate they give you is all you pay, no taxes on top of that...which in FL taxes on a hotel room are over 15%.
http://www.villas2000.com/frbvo/central_pf.php
Please PM me if you would like more info!