Continuity mistake: Doug comes out from the payphone and asks Carrie where did everyone go. When Carrie replies, the way she holds her glass changes between shots. (00:17:50)
Fixer Upper - S1-E12
Continuity mistake: When Doug is talking to Spencer in the subway, the people in the line behind him change instantly from 2 men to 1 man and 1 woman. (00:19:30)
Continuity mistake: When making a PB&J sandwich, the jar of peanut butter rotates by itself. Note the label. (00:09:30)
Visible crew/equipment: When the store clerk walks off from talking to Arthur an orange T marker is visible where he was stood. (00:14:50)
Road Rayge - S1-E9
Visible crew/equipment: When Doug's paper gets ripped up, look at Ray and Doug's feet. A blue and white tape marker is visible by each of them. (00:06:10)
Continuity mistake: When Doug falls off his chair his right arm is on the floor in one shot and on the desk part of the chair in the next. (00:09:10)
Head First - S1-E6
Continuity mistake: When Doug and Deacon are having breakfast in the kitchen, the door keeps changing from open to closed with no-one touching it. (00:08:30)
Head First - S1-E6
Continuity mistake: When the gang walk into Coopers, a woman and man are talking outside on the street. When the camera changes to focus on Arthur a second man has appeared next to the other two and should have been visible in the first shot. (00:03:40)
Visible crew/equipment: When Spence is leaving after dropping off the pictures a stage light is reflected in the door. (00:08:50)
Continuity mistake: When Doug Tells Carrie to pack for Atlantic City the cushion is either on or off her lap. (00:17:15)
Visible crew/equipment: Doug calls the phone number of the mystery guy, and when mystery guy answers his cell just a few feet away from Doug, two green tape marks are visible on the floor near Doug's feet. (00:16:30)
Frozen Pop - S2-E15
Visible crew/equipment: While Doug is scraping the windshield in the wide shots, the end of the street backdrop and production equipment are visible at the upper left side of the screen. (00:01:15)
Visible crew/equipment: Doug whisks Carrie to the boardwalk straight from the train after work, and when Doug points to the booth with plush frogs, a camera is visible on the left side of the screen as it moves out of shot. (00:17:20)
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.