St Lucia is the only "no-dogs" island on your list. Check noonsite.com for specific info.
- - Trinidad welcomes
dogs but if you are planning to fly in or out with the dog while the
boat is stored there - don't! It is a nightmare of bureaucratic hassles and expenses. Go back to
Grenada, store the
boat there and then fly out/in with the dog from Grenada. Besides Grenada has good direct to London flights.
- -
Barbados is not a cruiser friendly island only in that they are slanted towards mega-yachts. But you can
anchor off the town by the Yacht Club (open anchorage). Downtown is nice if small. Unless you need to stop there for US Embassy access for
USA Visa, I would suggest moving on to the Grenadines as soon as you are rested enough from the crossing.