Can I get FMLA paper work from my doctor in New Jersey if I am having my surgery in the Dominican Republic?

FMLA typically doesn't cover elective plastic surgery.  Speak with your company's human resources department on how to proceed.  

Medical tourism has becoming increasingly popular in recent years; patients  have been flying out of the U.S. for plastic surgery, lured by lower prices. 
However, a parallel trend has also appeared: plastic surgeons in the United  States are finding themselves treating an increasing number of patients who  plastic surgery abroad, correcting complications and errors. A survey by the  American Society of Plastic Surgeons found that 80% of the responding doctors  had treated American medical tourists for complications including infection,  contour abnormalities, and hematoma. Medical tourists are often led to believe that they will receive the same  quality of care for a lower price in a foreign clinic. But while it is true that  the cost of plastic surgery in some foreign countries is lower, this is often  because the quality of care and surgery is compromised. Such patients also seem  to neglect the possibility of complications and the need for a follow-up  visit. A number of patients have died in Dominican Republic for example following cosmetic procedures. In addition to the risks posed by sub-standard medical care abroad, medical  tourists must consider the risks of injections and implants in other countries.  The recent crisis with French breast implant maker Poly Implant Prothese (PIP)  exemplifies this problem. PIP used industrial- rather than medical-grade  silicone on their implants in an effort to reduce costs, a measure which  probably increased the danger of rupture. PIP implants have not been used in the  United States since 2000. Removal of these implants has been recommended by the  International Society of Aesthetic Plastic Surgery. It is often the case that medical tourists end up spending more  money because they have to pay to treat complications from their overseas  surgery.

Thanks for your question. While FMLA usually doesn't cover elective cosmetic procedures, it's going to be best for you to discuss your leave options with your employer's HR department. Good luck!