This is just for your information from my experience:

it's not too complicated to have delivery under family visit visa... after 7 or 8 months of pregnancy, you can start fixing appointments at womens hospital in Doha...for that u need referral from private doctor whom you have been consulting here in private clinics.
Delivery charges are as follows. C-section - 5400 (Cesarean birth), normal - 1000 and room charges - 400 per day.
once delivery is done, you can get birth certificate from womens hospital and then apply for passport from your embassy. there is no problem if your wife doesn't have RP. once passport is issued, go to immigration in garafa and apply for a family visit for your baby...this visa will be valid till your wife's existing visit visa. without visit visa for baby you cannot make exit.

trust above is clear....