Just as visa laws differ from country to country, so do the laws regarding your pets. Don't forget you also need to consider what policies exist for bringing them back into your home country, too.
If you wish to bring a cat or dog into Saudi Arabia you will need to obtain a Veterinary Health Certificate with an accompanying letter from the vet, and addressed to the Director of Customs, Saudi Arabia. The certificate must confirm that the animal is free from rabies and other diseases and has up-to-date vaccinations. The documents must be attested by the Ministry of Agriculture in your home country, and authenticated by the Saudi Arabian Embassy or consulate. Dogs can only be imported if they are defined as ‘guard dogs’ or ‘hunting dogs’.
On arrival in Saudi Arabia, animals have to be collected from the Saudi Cargo depot, where a customs declaration must be completed.