How small is the doggie? If stuck, ring around in advance because you may find that the hotel will make an exception for a 'lapdog' type. I've found that more than once.
You can be lucky.
My best example was, of all places, Claridges in London (yes, I really was desperate: the hotel of royalty, indeed!). Conversation at the hotel reception desk : Me " Do you take dogs in this hotel?" Reception " No,Sir, I'm afraid we don't" [ Receptionist looks over desk to see a tiny chihuahua] "Sir , I don't call THAT a dog. Come on in !" Trouble was, that the word got around and we were pestered thereafter by staff making excuses to visit the room to play with the dog, culminating with one arriving with a silver salver and entree dish, who said " Sir, chef thought your little dog would like some steak offcuts!" That spoilt the dog for life.Ever after that the litlte fellow wouldn't walk down Bond Street, without yanking on the lead to try to take me down the side street to Claridges, in the expectation he'd go in and get more treats! He never forgot. :)