Have you looked into the necessary paperwork you'll be needing to import a puppy into Dubai? Unless you're looking for an older pup, you may need to somehow find one that has already gotten their rabies shot.
Not many would choose to give their pups the shot at a young age. Though it does sound like importing from the USA, Canada, and/or Europe would be most ideal for you but you will be needing to acquire the appropriate import documentation/approval from the
"Ministry of Agriculture & Fisheries in advance of your pet's arrival which valid for 30 days from the date issued".
Import doesn't sound so bad for you.
At least there doesn't seem to be a quarantine period like some countries.
Good luck on your search!