The nearest clinic would be in Um Ghuwailina.
If you have been having your pre-natal check ups in a private clinic, they will be providing you a referral letter. However if you plan on giving birth in Hamad Women's hospital, you need to be registered first (if you do not already have a Hamad card). They only accept registrations in the morning. You need to bring a copy of your latest Kahrama bill among other requirements.
Good luck and have a safe delivery!