This may be a long forgotten post, but this update is for anyone who finds it.
It's called "DIG a journey into the earth" from 1972. The music is by Quincy Jones. Created by John and Faith Hubley. I too thought it was from "The Point," but I watched that this week and it was missing or so I thought. Both stories are about a boy and his dog. Not "A Boy and His Dog" by Harlan Ellison. (I miss you Harlan.)
I see that the links above no longer work, so here's a new YouTube link to the short. https://www.youtube.com/watch?v=2HbT1zXhRbk
I hope this helps someone, either the OP or someone doing a search for "Midnight Ride Down A Rock Bottom Road."
-No Fear Of Change-