Probably Cody Carlson. It's most likely the 1988 game at the Meadowlands, Jets won 45-3 and Moon either sat out a lot of the end or didn't play at all. I was there, can't remember who started for Houston. The other possibility is Brent Peace, who got limited action for them in 1988.
It is indeed a photo from the 9/18/88 game. Warren Moon sat out. He got injured in Week 1 and missed the next five games. Carlson and Pease both played in that game. I cannot make out which QB is in that photo. You can't even see the sleeve number at all. That would have helped. Carlson wore 14 and Pease wore 10.