Non-muslim men cannot marry a Muslim lady i believe
you will have to convert and face a tremendous amount of difficulty, this is not a normal event in Qatar. Other questions can arise about children, that's why u get married, in the past they could not automatically be Qatari! either way Qatar is changing, the fact that you can meet a Qatari lady and get to this stage in your relationship could not have happened in the past without male relatives deciding to avenge such an insult!
proceed carefully!