Not exactly sure whether you would be able to find one, but just FYI, whenever this topic has come up in the past, the consensus always is to not buy pets but rather adopt them. Some of the members that are knowledgeable about the issue, talk about how its a terrible industry out here and is rather cruel for the animals.
Check out the sandpit part of the forum, there is a sticky for pet adoption, with loads of good info/resource.
Animals sold here in Dubai come from battery farms from places such as the Ukraine. They have zero lineage, a lot don't even survive the journey and those that do are prone to a lot of health problems.
Contact the animal charities/shelters, they're not all Saluki crosses or problem dogs. Chihuahua's come up as people dump then when they haven't budgeted for relocation fees.
Please don't buy from a pet shop. Their animals are all from 'mills' - it's a dreadful, cruel trade. As Mr. Rossi says, there are many animal charities here and many, many dogs of all shapes, sizes, ages, pedigree and mixed breeds needing a loving fur-ever home.
Please don't buy a dog. There are no reputable breeders in the UAE - all the dogs are imported from puppy mills in Eastern Europe and bred in vile conditions. Many have health issues and come with doctored paper work.
There are literally hundreds of homeless dogs in shelters and foster homes crying for their furever homes.
Take a look at:
Animal Action Abu Dhabi
Sharjah Cats and dogs
RAK animal welfare
Dubai Dogs trust
Dubai Senior dogs project
All have dogs of every variety, age and background. They do get small dogs that are in need of homes.
Also remember that pedigree breeds are more likely to have health issues because of their inbreeding.