Are you talking about the flight attendants? Most (probably all) of them are not Qatari citizens. In fact most people in Qatar aren’t citizens and it’s similar throughout other Gulf countries.
EDIT: As for women not being able to travel outside the country (without permission), I’m not sure whether that’s the case or not in Qatar. I believe it is in Oman. Flight attendants and other people on work visas wouldn’t be subject to such laws, but they’d be at the mercy of whoever sponsored their work visa (though this affects males as well).
