Application forms for import permits can be obtained from the Ministry of Agriculture through a sponsoring employer. You will need to submit a copy of the pet's health certificate and vaccination record with the application.
Please see: http://www.qatarpetrelocators.com/importexport.php
Here you will find detailed information to assist you in preparing to move your pet. It's always better to have someone on the other end, helping you out.....I cannot stress this enough! When I first moved to Bahrain with my cat years ago, I ended up trusting informtion given to me by our company, and when I landed in bahrain, they confiscated my cat and put him into quarantine. So save yourself the tears that I endured.......and be thorough.
My dogs travelled into Qatar as Excess baggage, thanks to my Mother making the trip. This does not mean that they travel in the cabin with you though. They travel in the hold in the same way as when they travel as cargo. The difference lies in procedure, that is all. Depending upon your point of origin, travelling by cargo costs more. This is particularly true from and to the United States, as there is a flat fee for animals travelling as excess baggage.
Some airlines allow very small dogs or cats into the cabin with you providing you pay the fare. Just check out all your options first. Cargo has it's benefits too. Less hassle on your part, as the pet relocators will handle everything; and depending upon your route, some airports (eg Frankfurt) have a special facility to allow your pets rest time, a meal, some play and even grooming. These things need to be arranged in advance, so again, check with the pet relocators.
I am not sure what the procedure is if they travel as cargo, as I've never done it, but as excess baggage they are checked in just like your regular luggage. They are then loaded last on the plane, so that they can be offloaded first.
Please also note that in certain countries all animals must enter the country as cargo and cannot travel as excess luggage - regardless of whether you arrive in the country on the same flight as your animal(s) or not. This, for example, applies to all dogs traveling from to South Africa, as well as to all animals traveling from to the United Kingdom, Australia and New Zealand and other countries imposing quarantine restrictions for animals.
For long-haul cargo shipments I recommend using Lufthansa. British Airways is also very good, but until Qatar becomes recognised under the EU Pet Passport Scheme, I would avoid goind through the U.K.. Both airlines have dedicated Animal Reception Centers (London Heathrow and Frankfurt International Airports respectively), which will take good care of your four-legged friend during the stopover.
If your pet has to travel by Cargo, then my advice is that you contact Qatar Pet Relocators. Cargo procedures are not simple and require planning. QPR are the professionals, and know what is best for you and your pet.
Other Links for International Travel
www.iata.org International Airline Transport Association (IATA)
www.ipata.com Independent Pet and Animal Transportation Association International (IPATA)
http://www.defra.gov.uk/animalh/quarantine/pets/regulation/eu_reg.htm - DEFRA EU Regulation on the non-commercial movement of pet animals
Another good site is: http://www.pettravel.com/
Although, please bear in mind that sometimes information on the internet can be somewhat outdated; so it is always best to check with local resources that can be trusted (Vet, embassies, pet relocators) prior to your move to be sure that you have all the most up to date info.