I felt sure that Jane would have accompanied her sister Louisa and husband Albert Smith who had married in 1884 and also similarly disappeared. Sure enough here is the birth of their child Faith in the helpful NZ birth indexes. I later found Faith and her sisters listed in the NSW death indexes, unmarried. But there was a fourth sister not listed - perhaps she had married? Indeed Hope Bischoff is the one lead on this line.
This rather short article has had over 90 hits because of its title. I stand by the title. You can't google this stuff so it is the 'deep web'.