You can get married here in Doha with a priest and the marriage will be recognized by the Qatari state. But you need also to check with your embassies what paper they need (before the celebration and after) in order for them to recognize your wedding.
But the way you are writing your story, I am understanding that you want to get married in order to be able to live together. I would not advice to present things like that to the priest because he can of course refuse to celebrate your wedding.