Continuity mistake: When Carrie is unpacking the shopping at the start she holds up an empty bag that magically folds itself flat between camera cuts. (00:01:50)
Visible crew/equipment: When Doug arrives at the airport and we see the two gentlemen writing names on a board, everyone has tape markers at their feet. (00:03:20)
Continuity mistake: When Doug is writing on a board, he holds the board at the end or the top depending on the shot. (00:03:30)
Visible crew/equipment: When Carrie comes back saying she can't swap the flights, there are various tape markers visible on the floor. (00:19:00)
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.