Local custom (tribalism, not Islam) would prevent any Qatari from marrying her no matter how wealthy he is. Nothing is impossible but I don't see it happening. Its very difficult for a divorced Qatari woman to get married. But his woman also has many children, AND she has the accusation of adultery over her head.

The Tribe (and their standing in it) is the most important thing to the overwhelming majority of Qataris and gulf Arabs in general. If I recall correctly there is even a saying from the prophet Muhammad (peace be upon him) where he laments that the disease of tribalism will affect the Arabs until the day of judgment. Tribalism can be good for a few things but they really abuse it in this part of the world.

I also have a hard time seeing a non-Qatari (Arab or otherwise) marrying her as she has many children and the laws here don't really support Qatari women marrying non-Qatari men (especially if they are from non-Gulf countries).
It is likely she will eventually be able to get at least some social help from zakat funds.