Let's keep this inquiry active and see if someone comes up with some real info.

This doesn't sound like just a kids' song. This song sounds satirical, plus it is oddly universal and the lyrics are quite consistent over distance and time. I think this was originally a satire mocking something or it came out of the media somewhere.

My guess at the labor movement is based on the combined odd insertion of "goon" and the "scooping them up and bopping them on the head" violence against the mice, which normally wouldn't be associated with a rabbit.

My kids, who have a knack for being right about things, tell me it's an Easter song.