Neil Colquhoun (Auckland, NZ) collected "Soon May the Wellerman Come" in about 1966 from someone called F. R. Woods.
Mr. Woods, who was then in his 80s, told Colquhoun he had learnt this song and also the song "John Smith A.B.," from his uncle.

"John Smith AB" was printed in The Bulletin Sydney in 1904, where it was attributed to D. H. Rogers (and contributed by F. R. Woods?)

It is possible that D. H. Rogers was the uncle of F. R. Woods' and that it was he who composed "Soon may the Wellerman Come" and "John Smith A.B."

If Rogers had been born around about 1820, then he could have been a teenaged sailor and/or shore whaler around NZ in the late 1830s, settled in Australia, written the shanties in his later years as his composing skills developed, and then taught them to his nephew in his 70s-early 80s, some time between 1890 and 1904.