Yes it is the dollar on all the islands, just a pity the pound is now weaker against the dollar but take dollar travellers cheques with you and you can cash them on the ship at no cost plus you can shop around for the best deal before you go or use your credit card [Mastercard/Visa/American Express etc].
The currency on all P&O ships is sterling wherever in the world they are. Your account will be charged to you in sterling. US$ are widely accepted in the Caribbean islands but you may get change in local currency, so have some smallish denomination notes. Don't get confused between local dollars and US dollars. Some of the French Islands use Euros.
We have cruised the caribbean on various different cruise lines
and the c urrency on all ships was in U.S Dollarsand all Islands
accept US Dollars
P & O accounts are sterling - Princess - US Dollar.