Some breeds of dogs are restricted entry. So as long as your dog is not on the prohibited list, you should have no problems bringing in your dog on your own. However, since the 1st of August, rules have changed and all animals coming into or going out of Qatar must go Cargo. As a result you may find it a little hard on your own.

At least try to arrange for someone to help your with clearing your dog through customs, so that your pet doesn't have to wait hours.

Good Luck.

"Life is life - whether in a cat, or dog or man. There is no difference there between a cat or a man. The idea of difference is a human conception for man's own advantage." ~Sri Aurobindo