Dear Friend,
Don't worry you have 3 months to process the visa from the date of birth of your baby, birth certificate will be issued within one week time and the best thing what you can do if the passport is getting delayed to issue take a temporary pass port and go for the visa, once you have birth certificate and passport within one day you will be able to get the visa

(I did all of those for my daughter before 5 months)
Enjoy with your sweet little one

Thanks

Click on bellow link for more details

http://portal.www.gov.qa/wps/portal?New_WCM_Context=/wps/wcm/connect/cnt...