When it gets down to it, there are not many marriage options for Qatari women.
Also, marrying a South Asian, East Asian or African man, Muslim or not, would be extremely frowned upon and would probably limit the social and professional life of that woman and her immediate family.
A Qatari's professional life is very closely tied to their family standing, since most positions of power are in government or government sponsored entities (oil and gas or Qatar Foundation).
I lived in Qatar for some time and had quite a few single female friends and colleagues. Simply stated the law allows Qatari women to marry foreigners, though it is difficult, but they give up certain rights, like their children cannot be citizens.
Also, if a Qatari woman marries a non-Qatari or a Qatari from a "lower family," (there are 4-5 "politically accepted" families in Qatar), she limits her professional and social life.
You will never be given a top-post in a government agency or important government company, like QP.Marrying a Saudi, Emirati or Kuwaiti can also be limiting in your career especially, since you will no longer be "trusted." Also, there is a competitiveness between these countries and the idea of a male Saudi marrying a Qatari woman can be insulting and thus socially unacceptable.In an open discussion once on whether Qatari women should more easily be able to marry foreigners, the Qatari males exploded in objections with stories of Saudi men swooping in and stealing away all the women. When Qatari women do marry other Khaliji foreigners, their family usually has close ties to that country - for example there are a lot of tribes in Qatar with close family in Saudi, so they would be more likely to marry a Saudi.Really the topic is much more complicated than just nationality.
Tribe or family is more important than nationality.Qatari of Yemeni descent is sometimes just as bad a marriage prospect as a non-Qatari.