Hello Barry,
The tune is "Beautiful Dreamer" and anyone who listens to both songs can easily hear that it is. The first time I heard "Pub With No Beer" -- when it was first played on the radio -- I noticed. I must have been among the first to notice.
The words are a poem by a cane-cutter in Queensland, I believe, but I don't know the reference off the top of my head. Someone's sure to beat me to it.
Cheers, Joy