I don''t know for sure but I would guess that you''d have a fair amount of red tape to deal with. When I last went, eggs were held in suspicion. This is not to say that you shouldn''t go. Leave the pooch home and enjoy one of the last countries without a McDonalds or Hyatts.
Friends of ours spent 3 months in Cuba last winter aboard their 30 ft. motor sailor. Their crew included their dog. As far as I know the only requirement was to have a veterinarian inspection upon arrival.
All you have to do is give them a little US $$$ and the dog will be fine. We have done it several times with no problem. Even took the dog everywhere we went. Marina Hemmingway in Havana is where we go. Popeye
I know several crew who have had no problems with dogs in Cuba. A veterinary inspection is standard on arrival.
By the way, be very careful about spreading around those $U.S. In some cases it may help. In others in may get you in a great deal of trouble. At any rate, what is much more important than money is attitude. On a personal level Cubans are generally an open friendly people. If you are the same, you will encounter few problems.
Also, if being close to Havana is not important, think of entering Cuba at Varadero which has perhaps the best marina in the country. This choice will partly be determined by who you are --- Hemmingway is party-central, Varadero more quiet and suited to a family.