i don't think there's a problem with sponsoring your child here being married to other guy, but just to make sure, check Qatar counsulate in cyprus(if any) or the nearest, and also make sure ALL legal papers are stamped by the ministry of foreign affairs back your home before coming.

with your salary and your partner's you can easily find a furnished villa in a decent compound with social club and swimming pool, it's now for QR 10 K+ according to location and facilities.

you can always live with your partner here without being married, it's not legal, but he can rent an appartment and so can you, and then just live together in one. just make sure both apparments get one of you to visit once in a while, and keep paying the rent on time, and don't take appartments from Qataris directly, just try to get it from a real estate office, in a big building with lot od bachelors in it.

Yalla!