So I dug around a bit.

The YouTube video was incorrectly titled which led me to the wrong date.

“Star trip” episode was the second episode of season 1. Aired Sept 18, 1967. It’s not this video. That one had different actors. Much lower production value.

This video I linked apparently aired Dec 6th 1991. I was unable to find a title of the sketch.

https://thedaviddesk2.blogspot.com/2023/01/reconstructing-carol-burnett-show-part_16.html?m=1