You are very right to be worried.
In Qatar, the husband is the head of the household. He'd be required to raise all his children as Muslim, they cannot be allowed to be agnostic. Her daughters will, as a result, grow up in a much smaller & sadder man's world, where they are considered weak and inferior. So your granddaughters will be covered up in public and controlled/protected by a male guardian.
What if her daughter wants to leave Islam, or becomes a feminist activist, or is same-sex attracted? Apostasy is still officially punishable by death under Qatari law. Gay sex is a prisonable offence. Government permission is required to hold public meetings, and criticism/dissent is also a prisonable offence.
What if her husband decides to take a 2nd, 3rd or even 4th wife? As is his right in Qatar. The choices your daughter makes now could result in very great misery for her future children as well as herself.
You are desperately worried for her happiness, now. And later she may similarly desperately worry for her own daughter's happiness.
"Women must obtain permission from their male guardians—who may be fathers, brothers, uncles, grandfathers, and, when married, their husbands—to exercise many of their basic rights, including to marry, obtain a government scholarship to pursue higher education, work in many government jobs, and obtain some reproductive health care. Women also cannot act as guardians to make choices about their children’s lives. At the root of these discriminatory rules are laws, policies, and practices that deem men as heads of households and as legal and social guardians of women."
This is a very interesting report. And usefully includes lots of personal experiences which makes the risks seem all too real:
https://www.hrw.org/report/2021/03/29/everything-i-have-do-tied-man/women-and-qatars-male-guardianship-rules