Fairly recently Fed Ex put a mini hub in San Juan for the Caribbean and it's made a real difference in ship times. The Turks & Caicos likewise are getting next day service out of the US.
Just keep inn mind that receiving anything in the DR through Fedex which requires the ricipient to pay duties and taxes is a hassel(sp). Otherwise, everything I have sent to the DR usually takes only 1 or 2 days to get there from the US. The easiest way to get around the delivery issue when duties and taxes are due is to bill to a fedex account number. Otherwise be prepared to wait.