Hello Christine,
Found that a Thomas DISHER aged 26 arrived as an assisted immigrant on the Duke of Westminster on 8 Dec 1884, on QLD Archives Index. Also found the gavestone of Thomas Daniel DISHER and son Alexander Sharp at Irvinebank NQ on Cemindex. Also found LDS reference to his parents and 4 siblings at LDS Bx C119211 but James was not listed, but we know his DC said they were his parents.
Checked shipping mid 1887 to late 1888 for James DISHER but no luck [volunteers are working to complete lists]. Found James, Agnes and Adelaide DISHER in BCC's Toowong Cemetery.
There is still a good chance you will hear something from another Rootschatter.
Neil.