As I see the answers are quite different and confusing I recomend you to check the orphanages in Qatar they can give you accurate answer and complite details of what you need,you can adopt expat children but you can not adopt Qataries. If you are not muslim the marriage, adoption, divorce law are different so it isn't an issue. But what can be an issue is the high fees of adoption, the time the procedures can take and the financial proofs,family psychological history, background checking, etc.

If you don't have much of a luck in Qatar you can always check all those asian and african poor countries around Qatar where procedures can be easier and fees cheaper.

Out of all the answers I can say Ummjake is the most accurate.

Good luck!