For the family residency visa, you (being the expatriate worker) need to have a "Work Permit Visa" and have a salary of over Qar. 10,000

Both of these would allow you to apply for family visa under your sponsorship (as head of the family), and there is no harm in moving your application to the Immigration department.

If your family visa application is not accepted, you need to speak with one of the senior officials at the main immigration department (generally sitting on the 1st floor), who listen to such matters on a regular basis.

Please also go to the Main Immigration department located in Gharaffa area personally one day, that would give you more information and procedure.

Good luck