I doubt things have changed that much. We left Dominica two years ago...but here is my .02.
We brought our dog with us and he was miserable. I ended up bringing him home after two semesters and he stayed with friends. I would reconsider bringing your dog....especially if you are coming without a spouse, bf/gf. The power goes out alot and your pet will be stuck inside for long hrs if you're in class. You may not even know if the power is out and for how long.
Now, if you still intend to do this...here is what you will need. You must contact the housing office BEFORE you come. They can help you narrow your search for landlords willing to let you bring your pet. Or, I think there is now a housing site and it says if they allow pets. Search that on the Ross website. There is a quarantine. A BIG FAT joke, but you have to pretend to follow this. The vet....(Dr. McIntyre?)you have to fax all your pets records, and health certificate from your current vet to him. He will sign some documents and fax them back. You MUST have these on arrival at the airport. No papers, no dog. Also go to: http://www.aa.com/content/travelInformation/specialAssistance/travelingWithPets.jhtml
Read it very carefully. There are breed restrictions along with weight and size of the kennel. It is a big PITA.
The quarantine. You have to have a fenced in yard or a large balcony. Supposedly the vet will come check up on you but we never saw him until it was time to leave. We had to get a health certificate for the way home. Again, make sure you read the AA website. There are certain times a year that the pets cant fly. It if is too hot or cold they will NOT under any circumstances allow your dog to fly. I know this personally. My trip home was cancelled because my arrival city was below 30 degrees. They do not care that you have to pay the extra $100 to change your ticket. Of course if your pet fits under the seat with you, you will have no problems. Good luck.
ETA: You also need to think about your arrival and departure in Puerto Rico. If your flight is delayed/missed/cancelled like ours was it is a complete NIGHTMARE to find a hotel in PR that allows pets. NIGHTMARE I say!!!!!