Go to National Health Authority Bldg. right beside Lulu Center, opposite Hamad Hospital, along Rayyan Road, before the Sports Round-about.

Fill up the form available at the entrance, they're open Sunday to Thursday. Make sure you have a copy of your passport, your wife's passport and discharge certificate from the hospital. They will ask how many copies you require, you pay at the Cashier and then they will advise you to come back after a week to collect it there if there's no issue about wife sponsorship (better if she's under your sponsorship to avoid any hassles). You will also get a phone call verifying all the details before they enter the data on the birth certificate.