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1. Get the stamped/completed form from hospital and go apply for birth certificate from Hammad hospital (female section). It will take one week.
2. Go to embassy, fill out passport application and submit with copies of Iqama, Passport, Pak ID cards of both parents.
You will get the passport with one year validity only. with some luck, You can get the passport next day once you have submitted all the documents.
Congratulations on new baby and good luck.
Better call or visit Pakistan Embassy to get a concrete piece of information.