Without marriage she became pregnant in Qatar makes the case very critical. in my opinion consult with the lawyer he can guide u in a better way than others or QL.

but what i understand is there should be a husband or any proof of husband if he is living outside of the country at the time of delivery as a name of the father of the baby just to complete the paper work. otherwise it will become illegal and might be reported to police.

if you are from western country, police and authorities know very well about the baby without marriage is common there. but if she delivers a baby here in qatar she should have a proof of husband even she get married one day before delivery.

but i suggest to consult with lawyer if u can afford.