Wa Aliaikum Wassalam,
1.Baby original Birth certificate issued by Supreme Council of Health
2.Original passport for the baby
3.2 pp size baby photograph
4.your marriage certificate original + copy
5.your QID original + copy
6.Your Passport Original + copy
7.prescribed filled application
8.debit/credit card for fee payment
take all the above said documents and go to any immigration office, it will be done with in 10 mins, (but you have to wait in queue for an hour or more)
http://www.qatarliving.com/visas-permits/posts/rules-changed-rp-new-born...

http://www.qatarliving.com/visas-permits/posts/baby-visa-rp-stamping-pro...