How exciting to have a new puppy to sail with! As much work as it may be to sort out all of the logistics before you leave the USA, the companionship and good distraction that a furry creature can provide is well worth it. As others have mentioned, Noonsite is a great resource for fact-finding. Having your documents in order (multiple hard copies and electronic copies) to send or e-mail to the appropriate animal quarantine services of different countries is probably prudent. We sailed with our dog from Mexico
with stops in Hawaii
with minimal bureaucratic hassles as we had prepared many months before our departure. As we leave Japan
for New Zealand
with many stops in between, we opted to fly him back to Canada
. In order to meet the quarantine requirements for New Zealand
we would not have been able to have him off the boat for any period of time. That would have meant almost 10 months of being restricted to the boat which we couldn't imagine. We may have been able to sneak him off the boat in certain places but weren't prepared to risk any penalties to the dog or ourselves as foreigners in another country.
Wishing you all the best