Yeah, they don't allow dogs in the backcountry of the national park.

But there are doggy day cares in Moab.
http://www.gomoab.com/moab_kennels.html
http://moabdogadventures.com/mda-site/
http://www.moabpetcare.com/

My dog is old and mellow enough I will just leave her in the room, hang a Do Not Disturb sign on the door so the maids don't go in, and she will snooze the day away on her dog bed, just like when I am at work.