If you are talking abour renting a condo or apartment, you should be able to find a place. However, you are likely to find there are rules about what the dog may do. In the condo where I live in Sosua there are rules prohibiting the dog to run free and from going into the commons areas--especially the pool area. The dogs we have in our complex are inside the condo unless under the owner's control.
Of course, you wouldn't want your dog to run free anyway. There are a lot of street dogs that would be very interested in a newcomer.
Is your dog a street fighter? Well, be ready to meet our Mike Tysons and World Wrestling of the dog world. This is a stray dog paradise. Our "hueveros" are very friendly to humans and give a fine welcome to newcomers. But if your dog likes to pick a fight, even our starved four leggers can give you a run for your money.
I've never had a problem. Many Dominicans have dogs to allert them to burglars. Disease is a problem, though. Have the legal papers made by your vet for intl. travel and get a good vet as soon as you arrive for frequest checkups and problems. A great many homeless animals on the street that spread disease when you walk your dog.
We have a large population of a new species....the three-legged dog. You see, most Dominican stray dogs have a habit of sleeping under cars for coolness. They sleep so profoundly that they sometimes cannot hear or feel a car engine start. That's when the fourth leg becomes a "hanging chad".
Unfortunately I chadded one recently. I still feel bad because everytime he sees me he runs, like I did it on purpose!!
Well, be careful, few dogs in DR survive cars and trucks. All it takes is one second off the leash and....yergone.