Continuity mistake: Carrie tells the preacher that she and Doug met at a bar. When she hears the lie about her falling on Doug as a kid, she believes it and acts as if that was their only meeting before the bar. But in the episode "Road Rayge", she mentioned a junior high school dance where Doug asked her to dance.
Visible crew/equipment: In the church just as the minister tells Doug and Carrie to take a seat, two white tape markers are visible on the red carpet. (00:05:30)
Continuity mistake: When Doug is speaking to Spence and Deacon about Carrie throwing up, Spence takes the cap off his beer which reappears a few shots later. (00:02:45)
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.