According to the report at www.telegraph.co.uk/travel/main.jhtml?xml=/ travel/2003/10/04/etcase04.xml there are conflicting views on this matter, and the only way you will get a definitive answer is by asking the Consulate of the Dominican Republic. But, as you will see from the report, you should also check with the airline concerned, as they may insist on a letter from the other parent, authorising the child's journey.
ITravelled to the dominican republic in december 2003 with my 12 year old daughter....i am a single parent..although i carried her birth certificate i was not asked to show it.i did not have any other documents. She is included on my passport. This also happened in mexico at easter after all the panic about single parents travelling with their children no one queried the fact i was a single parent