My dog goes back wards and forwards from to UK. I have done the process my self each time with no problems. Your pet will need a pet passport inc the rabies vaccination. You then need to apply for a import certificate, can do it on line. Mine flies cargo with emirates you can pick them up after about an hour after arrival, Emirates will point you in the right direction for customs/national vet in the cargo terminal. National Vet now also accepts UAE Visa cards.
Cheers
10d