Your wife can travel till 28 weeksof pregnancy on any airlines but you need to have doctors travel certificate stating how many weeks she is pregnant & she is fit to travel.

Secondly if your wife goes for delivery out of qatar you need to bring the child back within three months since the birth of child. Make sure that the birth cerificate of your child is attested. 

Then you can apply for child visa in Qatar within a week after your child enter.

And ask you wife to carry attested birth cerficate of you child & your Qatar id copy while coming back to doha as they will ask her at the doha immigration

Hope it helps u.