Transporting animals by sea from country to country is a huge impracticality. Animals carry diseases that may not be present in the countries you visit. Countries frown on this, especially the US. You may even find your animals subject to quarantine upon return. If it is essential that you land; you may find that your choices are extermination of your animals or no pratique.
Animals at sea are a huge pain in the neck for, what should be, obvious reasons. If you must have animals on your boat I would advise you to take stores south of Hatteras. With the aid of a little lax house-keeping you will soon have cockroaches the size of, well, bull terriers.