Visible crew/equipment: When Carrie gives Doug the card, the top of the set is visible behind them. (00:10:40)
Visible crew/equipment: When Doug says about Kelly being in the wrong he puts his arm up in the air which shows the top of the set and some equipment. (00:14:00)
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)
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)
Visible crew/equipment: When Doug gets the beach ball, all the stage lights are reflected in it. (00:14:00)
Visible crew/equipment: When Doug and Arthur arrive in the City to talk to Carrie, yellow tape markers are visible on the floor by Doug's feet. (00:15:10)
Visible crew/equipment: We see Doug slide past the camera at Carrie's hospital appointment. When he does, a boom mic is reflected in the picture behind them. (00:11:50)
Visible crew/equipment: Near the beginning when Doug comes into the kitchen and smashes the cake with the watermelon, you can see a stage light reflecting in the door window 3 times as it swings open. (00:00:10)
Visible crew/equipment: Throughout this episode you can see stage lights reflecting off Carrie's glasses - most notably in the bedroom when Doug finally convinces her to join the party. She looks toward the camera and a series of stage lights are reflected very evidently. (00:16:25)
Mean Streak - S4-E3
Visible crew/equipment: After giving an interview Doug walks over to Deacon and a tape marker from earlier in the scene is visible on the floor. (00:05:20)
Mean Streak - S4-E3
Visible crew/equipment: Doug is debating smashing the woman's parcel. As she opens her door a black tape marker is visible on the floor. (00:15:50)
Visible crew/equipment: Carrie begs Arthur to move upstairs, when she does, a tape marker is visible on the floor by the stairs to the basement. (00:05:30)
Visible crew/equipment: When Carrie walks into the bedroom at the start, 2 tape markers are visible on the green carpet. (00:06:55)
Visible crew/equipment: When Doug says he doesn't want to look after Arthur in the bedroom, there are 4 tape markers visible on the floor at the foot of the bed. (00:14:30)
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)
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.