No problem.
The only hotel-casino properties we're aware of that admit pets are Green Valley Ranch, Red Rock, Lucky Club (formerly the Speedway), and the Westin Casuarina. The Four Seasons also admits pets, as does the Super 8 Motel that's affiliated with Ellis Island. A number of other non-gaming properties also admit pets -- you'll find our Pet-Friendly section in the Hotel Guide in "Hotels & Rooms" and also duplicated in the "LVA Visitor Guide."
Many of the properties that admit pets charge a fee (sometimes a refundable deposit, sometimes a non-refundable one, often a nightly charge, and frequently a combination of these). It's common for a one- or two-pet-per-room policy to apply and certain weight restrictions are often imposed too. Twenty to twenty-five pounds is the common maximum, however, so your 15-pound puppy should be fine. You'll see in our listings, which we just updated, that a number of properties will accept pets that weigh 40 pounds or more, but several will not permit certain breeds of dogs, including pit bulls, Rottweillers, and Dobermans.