The first thing is to get a birth certificate

The procedure is simple.

Near the entrance inside Hamad Women's Hosp (On the right hand side when you enter). There is an office which issues Birth certificate, collect the application forms from there , the staff will tell you which documents are required. (
The documents are mostly Copies of Passport, Visa page and ID. Along with a Copy of a Green booklet(CHILD IMMUNIZATION CARD) the hospital will issue for your baby. check if any more documents are required i cant remember all.

Ask for 2 Copies of the birth certificate. There is a fee, so keep your debit card with you. You will get the certificate in a week. check all details.

Next is to apply for a Passport for your baby. Check with your embassy for details.

After receiving the passport. You can apply for Visa.
Go to any typing centre with all 3 passports and get an application in arabic with Husband as sponsor (just tell them , they will do the rest). ask them if you have any doubt.

with
the application , Passport size Photo of baby.
birth certificate
Parents Passport ,Visa and ID copies.
Apply @emigration department family section, take a token go to the last counter on the right for verification & signature and wait for your number.

Thats it.