In general, travelers visiting Alaska [1] should leave their pets at home. Dogs may be good hiking companions, but if not kept under control they could bring a bear charging in your direction. Most hotels do not allow pets, and even those that do typically tack on an extra charge for the privilege.
Folks driving up the Alaska Highway—particularly RVers—frequently bring along a small dog or cat, but a current rabies certificate is required when crossing into Canada.
Links:
[1] http://www.moon.com/destinations/alaska