These are the regulations for bringing a dog or cat back into the USA from your Alaskan adventure.
"CDC regulations govern the importation of certain animals capable of carrying diseases that can be transmitted to humans (zoonotic diseases). Pets taken out of the United States are subject upon return to the same regulations as those entering for the first time. These regulations apply whether the person bringing the animal into the United States is a U.S. citizen, legal U.S. resident, or foreign national. CDC-regulated animals are subject to inspection at ports of entry." https://www.cdc.gov/.../bringing-an-animal.../index.html https://www.cdc.gov/importation/dogs/index.html
CDC requires that cats appear healthy upon arrival to the United States. Cats are subject to inspection at ports of entry and may be denied entry into the United States if they have evidence of a zoonotic disease. If a cat appears to be ill, further examination by a licensed veterinarian at the owner's expense might be required before the cat is allowed to enter the United States. Cats are not required to have proof of rabies vaccination for importation into the United States. However, CDC recommends that all cats be vaccinated against rabies, and your U.S. destination may have additional requirements.
The state of Alaska does require a current certificate of health to enter Alaska from Canada. Not all veterinarians are USDA certified, but those who are, through the National Veterinary Accreditation Program (NVAP), are authorized to complete and sign international health certificates for animals, especially for export. Ask your vet if they are certified. They can help you through the process. Bringing Dogs, Cats, and Ferrets to Alaska
We would recommend a Kennel Cough and Parvo shot. Your dog will be in many places sniffing and scratching where hundreds of other dogs and critters have been.