Visible crew/equipment: During the flashback, when Carrie walks over to Doug at the side of the house, and he zips himself up, in shots facing Doug, a crew member and production equipment are visible on the right side of the screen. (00:20:10)
Visible crew/equipment: During the flashback, while Doug is waiting on the porch Carrie rushes out then gets into her car to take off, and in the next shot facing the front door, the reflections of the camera operator, wearing a white baseball cap, and the camera are visible on the window. (00:12:35)
Visible crew/equipment: When Doug sneaks out of Carrie's house and finds her having a cigarette by the car, a boom mic shadow can be seen on the bush beside Doug. (02:53:45)
Answer: To answer the question directly. Carrie and Doug do not have a biological child during the show's main run. In season 3 or 4 finale (cant remember which) Carrie has a miscarriage. Later on in the show they find out Carrie has 1 working ovary. Thus reducing the chance of them conceiving. By the final season, they couple agree to adopt from China and go to collect their child in the show's final episode. While on the flight back from China it's revealed that Carrie is once again pregnant. However the last scene of the show is a flash forward showing that Carrie goes full term with that child and they are struggling with both kids.
Ssiscool ★
Adding on to this answer, I read somewhere that producers were afraid of the show having a "before baby" feeling and then an "after baby" feeling. Some fans feel that main characters, or the show in general, decline in quality after a major change. For example, Jesse and Rebecca on "Full House" after they had twin sons, and Daphne on "Frasier" after she married Niles.