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If you decide to bring your pet(s), please ensure the accommodations you secure for your visit allow pets on their premises. Also be aware that in some of the tourist destinations there may be stray animals, particularly dogs. If you are in fear of your pet being around stray animals, it may be wise to have your pet looked after at home during your visit. If this is not a concern, please be aware of the following requirements to bring dog(s) or cat(s) into the Dominican Republic:

A Veterinarian's certificate of vaccination against rabies , issued at least 30 days prior to entry into the Dominican Republic.
A Veterinarian's certificate of health issued within 14 days of arrival into the Dominican Republic.
If the above requirements are not met, your pet may be held in quarantine for up to 30 days, depending on your country of origin.
Upon arrival at any Dominican Republic Airport, ask for the Animal Control Person ('Sanidad Animal' in Spanish). This person will review your Veterinarian certificates and fill in the official pet entry permission form required at a cost of approximately US $10.

From Bringing Animals to Dominican Republic by Hispaniola.com