Character mistake: In the opening scene, Doug call Carrie "Kel" which is Deacon's wife. He calls her that when he's saying they should just get a new grill.
Visible crew/equipment: When Carrie goes into the kitchen and Doug is seen through the window getting burnt, the boom's shadow can be seen moving along the wall by the window. (00:14:45)
Visible crew/equipment: When Carrie walks in and sees Hollie for the first time in the episode, a boom mic can be seen following Carrie across the kitchen. (00:07:00)
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.