If you're planning to travel with your pet into another country, you will need to find out what regulations that country has regarding the import of pets. Every country has their own set of regulations. Leave yourself lots of time to get the documentation together before your trip.
Many countries will require that you provide a pet health certificate issued by an accredited veterinarian. Other documentation may also be required.
Bringing a pet into the United States: contact the U.S. Department of Agriculture (USDA).
Bringing a pet into Canada: contact the National Animal Health Program.
Other countries: contact their embassy or consulate, who should be able to point you towards the appropriate authority.