Unless you are moving to the Virgin Islands [1], leave your pets at home. You will have to overcome serious administrative hurdles to bring your animal to the British Virgin Islands, and it is not much easier to get a pet into the U.S. Virgin Islands. It will not be easy to find a hotel that will let Fido stay with you.
Links:
[1] http://www.moon.com/destinations/virgin-islands/discover-the-virgin-islands