Congrats!!!! Great news.
Funny enough, I had the same discussion with a lawyer about 2 months ago.
Either way, it is illegal to be pregnant and not in marriage or to have the baby and not be married. The illegal part apparently (on just being pregnant) is that it means you've had 'relations' outside of marriage which is prohibited.
Most places don't go that far... however, I've heard rampant stories about Hamad hospital not only requiring copies of marriage certificates (ok, fine) but questionning even further as well.
Fact is, you're married now so I wouldn't worry about it. But do avoid hospitals or doctors that this could be a questionable area.
Best to avoid the possibility anyway ..... look for a more ex-pat type of hospital (Al Ahli is a good one as are others) .... you won't be questionned at all except for 'when you were married' and thats it.
Good luck and don't worry.