Opes, my Bad,,, i miss Understand.. Dont wrry if you have the Marriage Certificate which is Stamped by ur embassy and MOFA and also u have Arabic Translated one with same Stamps from MOFA and Chamber of Commerce (for Arabic one u will need stapm from Chamber of Commerce) then from MOFA and then you r Good to all.
you will only Face a small messup in it.
I mean, after the Birth maybe in HMC direct you will not get the Birth Certificate.
STEPS to get Birth Certificate are :
1: take your Marriage and passport and QID copy along with Green card which the Room nurse will give after birth.
2 : Visit the Supreme Council of Health near Medical City.
3: fill the Forums. and 20 Qr per Copy of Birth Certificate.
4: they will give u a Paper with Date that you will need to goto the CID Dep which is on Salwa Road near INDUSTRIAL Area.
After That (from CID )
1 : they will give you the Birth Certificate only 1 Hard Copy. for Additional copies u will goto Supreme Council of health again and they will take 10 minutes to give u copies.
he Copies are Recommended. ( make 2 Eng and 2 Arabic Better)
2: Bring Birth Certificates to MOFA and Stamp it. 1 stamp p/Copy 20 QR.
3: goto your embassy along 1 original birth certificate , copy of parents ID passport and make passport,
4: goto Immigration to make for her/him Qatar Visa.( take all the Papers original with u and copies)
5: go back to CID and Close the file after u get QID Stamp on new baby passport.

NOTE : Every Official Place you go, take Original DOCS and extra 2/2 copy of each DOC to avoid problems of missing DOCS.
Good luck..