In Qatar every birth has to be registered even if it’s of foreign nationals’.  Babies born to expatriate parents are not entitled Qatari citizenship. But a Qatari birth certificate is issued. Expatriate parents are responsible for registering their child’s birth with their respective country’s embassy.

All births in Qatar should be registered at the Women's Hospital, which is next to Hamad General Hospital on Al Rayyan Road. The hospital where the delivery took place will issue 2 letters to obtain birth certificate. 
    Bring the two letters, along with a copy of baby’s vaccination card, both parents’ passports, copies of parents’ Residence Permits (or entry visas) and marriage certificate of parents to the Women's Hospital.
    Complete the required paperwork.
    Pay appropriate fees.
You can get the birth certificate from Women’s hospital on the same day. It is issued in Arabic. As you have to present the certificate to your embassy, it has to be translated to English or to any appropriate language.


Next,  you have to take your baby’s birth certificate to your country’s embassy for complrting the birth registration and for applying the passport for your newborn (or to add the child to your passport). You must do it in order to get the residence permit for your child. You should check with your country’s embassy to know the required documents. Usually, Qatari birth certificate, Parents’ passport, parents’ marriage certificate, passport photos of the baby etc. are needed.
Residence Permit for the Newborn

You may get your child’s passport in a few weeks. Once the passport has been issued, you can apply for the newborn’s residence permit. Submit the requisite documents and pay the visa fee at one of  the immigration service centres.
Documents needed:
    Child’s passport and a copy
    Sponsor’s original ID
    Copy of Qatari birth certificate
    Copies of parent’s IDs and RP pages
    Copy of Parents' marriage certificate
    Fee- 960 QAR (for three years) to be paid via debit card (cash not accepted).

You can stamp it for a year/ two years. The fee is accordingly lesser. Also, no ID cards are issued for children.
You can get the full details of the process from the Hukoomi website. You can apply online.
Your sponsoring company can help you with the visa application. You have to complete the entire process within two months of birth.
If the mother delivered her baby in her home country and wants to come back to Qatar, the baby can come to Qatar on a Visit Visa. But within two months parents need to apply for the residence permit for the newborn.