I think it is Australian. My brothers and I had a record player when we were itty-bitty in 1954 or so. I was five years old. That record was one of our favorites.
It is weird that I can still recite most of that song.
I never heard it as a song, just read the poem when I was a kid. Can’t remember more than the first few lines, though.
I suppose it’s online somewhere. Who knows, maybe the song’s even on Youtube.