Few tips:

Be considerate of the fact that many people in the BVI dislike/are afraid of dogs
I assume you have a lifejacket for your dog, if not, get one
Your dog will probably be much thirstier than usual, so watch the water bowl
Second the freshwater rinse as suggested above, or they will be uncomfortable and itchy
Make sure you bring a blanket or something for your dog to sleep on
Bring chew treats etc with you, they aren't always easily available here
Don't ever leave the dog on the deck if you leave the boat. Shut them in the galley with ventilation, cabin doors shut
Check with any business before you take the dog ashore. Personally, I don't take mine ashore at Jost
For your peace of mind, buy a poison kit from Canines Cats and Critters opposite Nanny Cay before you start

Ime most dogs love sailing and are pretty easy shipmates. Have fun!