Funny, reading this thread.. I never thought of the song as a Children's Song. I remember it when I was in college, not singing it at summer camp. The song was very touching in the movie, because Peggy Lee's character had a mental breakdown and reverted to being a little child, in her mind. The scene where she sings the song is very moving, and disturbing. Not a tv kid's show moment. But, I can understand why the song took on its own life... it's a fine song.
Jerry