Hi Dave- lots of folks bring their pets to Panama, and there is a process to do so.
First, you’ll want to check with the airline you plan to travel with to get specifics on their requirements.
Then you need to get an international health certificate from your vet within 10 days of your departure.
This completed certificate must be endorsed by the USDA, then authenticated by the Panamanian Embassy or consulate.
Another option (sometimes easier) in the US is to have the certificate Apostilled by the Secretary of State where you live.
You need to carry this completed document with you when you travel with your pet.
Three days prior to your arrival in Panama you may download and submit a Domestic Quarantine Form that allows you to take your pet with you from the airport. Without the required forms the normal quarantine period is up to 40 days. Once you arrive in Panama a vet will meet you at the airport to provide the documents you need for your pet to remain in Panama.
All the details you need are here on the IL Panama page:
https://internationalliving.com/country_clubs/panama/moving-to-panama/#pets
All of these steps include fees, so there is a cost involved. While it may be difficult to leave your pooch behind, for a short visit of a month or two it may be the better option. Then if you come back to Panama for a longer stay, you’ll be familiar with the country and you can bring your puppy with you.
I hope this helps, Linda