Visible crew/equipment: When Doug is outside talking to Deacon and Arthur opens the kitchen door, as the door swings back you can see all the set lights reflected in the glass. (00:08:20)
Visible crew/equipment: When Doug sneaks out of Carrie's house and finds her having a cigarette by the car, a boom mic shadow can be seen on the bush beside Doug. (02:53:45)
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)
Party Favor - S2-E13
Visible crew/equipment: When Doug and Carrie are arguing about Danny coming over, you can see a stage light (not on) through the door window. We can also the neighbours garage, which we know from many outside shots of the Heffernan's backyard, is not that close to the house. (00:01:50)
Party Favor - S2-E13
Visible crew/equipment: When Doug goes back to the house after unsuccessfully scraping the frost off the car, a stage light is reflected in the window to the right of the front door. As Doug approaches the door his own shadow passes over this reflection. (00:01:30)
Frozen Pop - S2-E15
Visible crew/equipment: When Doug is scraping the car, watch carefully and you can the the reflection of someone off screen behind the camera move. (00:01:10)
Dire Strayts - S2-E8
Visible crew/equipment: When Carrie asks what Deborah is like, on the cupboard door above Doug you can see the reflection of a boom mic moving around. (00:04:45)
Dire Strayts - S2-E8
Visible crew/equipment: When Doug says about watching the game at his on the big screen, a boom mic drops into shot very quickly. (00:01:45)
Move Doubt - S8-E8
Visible crew/equipment: Season 8, episode 8 "Move Doubt": When Carrie and Doug leave Kelly and Deacon's apartment, you can see the shadow of a boom mic on the wall to their left.
Visible crew/equipment: When Carrie and Doug head out to the garage the first time, a boom mic is reflected in the door's glass. (00:04:05)
Visible crew/equipment: When Carrie says about going back in time, a boom shadow can be seen moving over the wall. (00:02:30)
Visible crew/equipment: When Doug says that Carrie is making progress with her room, a boom shadow can be seen moving along the door. (00:03:30)
Visible crew/equipment: When Deacon comes to get his camera, after he walks toward the back of the house, you can already see the shadow of the mailman in the doorway.
Visible crew/equipment: When Doug and Carrie leave for their holiday, a stage light is reflected on the kitchen door. (00:09:30)
Dog Shelter - S5-E23
Visible crew/equipment: When Doug finds out that Rocky is in fact Rocky 4, a boom mic is reflected in the window. (00:10:20)
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.