You have many options:
1. Personal pediatricians office
2. Local Health Center
3. Abu Hamour Immunization Center.
Your pediatrician/private hospital will cost you quite a bit of money.
Immunizations are free at your local health center/Abu Hamour immunization center. Call which place you prefer (dial 180 for the number) and check to see if they have necessary immunization in stock. The only cost is 10QR for the immunization card if you don't already have one.