A dog or cat under three months old may enter Canada without any documentation as long as its owner accompanies the animal. In order to take a dog or cat over three months of age into Canada, you must show a certificate from a licensed veterinarian stating that your pet is free of rabies and is up to date on rabies vaccine. Ask your veterinarian for a rabies vaccination certificate, and make sure the doctor notes the breed, sex, color and weight of your animal. The certificate should also note the name of the vaccination used and the duration of its validity. After you display the certificate, you will be allowed to take the dog or cat into Canada right away.
Canada allows most members of the rodent family to enter without any kind of permit. Canada does not allow prairie dogs, Gambian pouch rats, squirrels or any rodent from Africa. Specific provinces have their own laws about which species may or may not enter. Alberta requires a permit for rats. New Brunswick requires a permit for any animal that is not indigenous to the area and "is a species of wildlife that in its natural habitat is usually wild by nature."
To take pet birds from the U.S. into Canada, you must sign a declaration stating that you have been in custody of the birds for the 90 days previous to the visit and that your birds have not come into contact with any other birds. You must also sign that the birds are your pets. The Canadian government will allow neither you nor any member or your family to bring a bird across the border under the pet bird provision for another 90 days. If you are taking birds into Canada from any country other than the U.S., you must provide the same information on a form you can get from an import officer. Take the completed form when you cross the border with your birds.
The Canadian government no longer requires documentation for most reptiles and amphibians. In order to import turtles or tortoises, however, you must obtain an import permit from the Canadian Food Inspection Agency and submit it to a CFIA import office. You can get the application for an import permit at the CFIA website.