Ced2's description of the dolls reminds me of seeing this song performed on TV by Rolf Harris. Being artistically minded he performed complete with the 'dancing dolls'. The dolls he had matched Ced2's description in that (as far as I recall) they were similar to marionettes, but with head and torso in one piece of wood, with 'loose' arms and legs, and each was on to a long piece of dowel attached at about shoulder blade level.
As this was on children's TV, Rolf explained the whole meaning of the song. I wrote to him requesting the words at that time, and (somewhere) still have his reply, which included a photocopy of a manuscript (literally. words and music hand written on staff notation paper! ) of the song . A search today has not yet turned it up, but I'm still looking.

Nigel