Charlie, you're a pretty darn good substitute for my failing memory. That song has been going through my head, and I couldn't remember who I heard sing it. It's on an album called From Where I Sit, recorded by Anne Dodson in 1993. On this particular cut, Sarah Ehrlich sings the lead vocal, and Anne sings the "Do your dog run rabbit" chant. It's a very good album, and you'll notice i've included a link to the album's listing at the new Mudcat Store. Lyrics to the song are close to what I posted, with the addition of the "rabbit" chant that Charlie posted.
-Joe Offer-