An outback murder mystery published in the 1950s makes me think of Arthur Upfield. I know he lived in WA for a while, and worked on No1 Rabbit Proof Fence (so he got out that way - 1929?).
The introduction to
Up and Down Australia says Upfield published some 250 short stories, most between 1931 and 1940 (
of which I've read 0). How such a story would end up in Hobart published under E M Delafield I do not know, but Upfield did get around.
Of course I imagine you have already considered (and probably discarded) this possibility, he just struck me as the most obvious candidate to fit the details.