Presuming the cats are adults and up to date with their vaccinations, all you need to do is get them Rabies vaccinated and keep a copy of the card to scan and email for the import licence, the vaccination must be done well in advance of travel. I recommend however that you obtain a UK Pet Passport for them while you are there, it means you will be able to travel easily to so many places such as all of the Gulf and all of Europe and, hopefully soon back to the UK. The only extra thing you would need to do that is get a Rabies serology blood test done and ask your vet to make up a passport. If you do not get the blood test done in the UK and then want to travel to practically anywhere outside of the UK you would need to get it done here and the blood will have to go to the VLA lab in the UK anyway, much more expensive as you have to pay for the courier to fly it back!
You need to get an export licence from DEFRA, any local vet will be able to do this as long as they are registered and if you have a pet passport they simply stamp and date the passport to say the animal is in good health and permitted to travel.
This end, contact either Doha Vets or Qatar Pet Relocators to obtain the import licence for you. They will need a copy of your passport and a copy of the vaccination card. Both of these companies offer a meet and greet service which I highly recommend. I used Doha Vets and was extremely glad to have an Arabic speaker who knew how to deal with the customs men, would have been a bit daunting without them.
I hope that helps.