It's a common question, and one that expat resource Living Abroad recently tackled:  what do you have to classify your dog as before you can move your pet to Saudi Arabia?

Most people do not realize that dogs are only allowed into Saudi Arabia if they are classified as "guard or hunting dogs."  This can usually be arranged fairly easily for pets like Rottweilers and hound dogs, but what if you have a Jack Russell or a Chihuahua?

From Living Abroad:

Dogs, regardless of their breed, may only enter Saudi Arabia if their paperwork describes them as watch dogs, hunting dogs, or seeing-eye dogs for the blind and hearing dogs for deaf persons. Cats and dogs that enter Saudi Arabia require a Veterinary Health Certificate and a letter from their veterinarian that is dated and addressed to the Director of Customs, Saudi Arabia.

We have moved pets with various breeds to Saudi Arabia in the past, even small dogs.  As long as the paperwork deems the pet is a guard dog, there are no issues.