Wow. I can't believe I just read through NINETEEN years of unsolved mystery around this song. From hunting around the web, I have to think it was of pre 1950s origin (just based on folks who have claimed to have learned it around or before that time), but alas... I am yet another commenter who does not provide a true answer.
I'm a Girl Guide in Ontario, where we still sing this song. I'm amazed at how this song seems to have travelled so pervasively! This has probably started a new compulsion in me... to open every song book and reader I see and check the contents. ;)
At any rate, thanks for what was an interesting thread nonetheless!