Hi, Celle -
Yes, we are related, but the link is a long, long way back. Our shared ancestor is William Cornhill, b 1797 in Oare in Kent.
He joined the army - the 7th Foot - at the age of 20 and served in Corfu and Malta in the Mediterranean for much of his career.
William married a girl named Martha from Wokingham in the early 1820s, and they had two sons - Joseph and William Jnr, born 1825 and 1826 in Wokingham.
William was discharged from the army while serving in Ireland in 1839 "worn out from his service" (according to his discharge papers!). He and Martha and their two sons returned to Faversham in Kent, where he died the following year of kidney failure.
The brothers Joseph and William both became bakers by trade - Joseph settling in Whitstable, and William in the Faversham area. I descend from William, via his eldest son, another William b 1848 - and you descend from Joseph, via his eldest son Joseph James also b 1848.
Agnes Golder was in fact Agnes Elizabeth Cornhill, b and registered in Eastry District in the quarter ending March 1881, born to Joseph James Cornhill and Hannah nee Darby. The 1881 Census lists her after her one-year old brother, John T, as age 2, but that should be aged 2 months. At that time they were living at 4 Chapel Street in Deal, where Joseph James was an unemployed baker. Birthplaces of some of the older children, including John T, indicate that the family had just returned to Kent following a period in London.
Subsequent Censuses show her as Agnes Golder after her mother Hannah moved in with Lewis Golder and took his name for herself and her Cornhill children. When Agnes married Daniel Mildred in Woolwich q.e. Dec 1905, she married as Agnes Golder.
As for Joseph James, most of what I know is already posted above or on the other thread linked to this one. He and his brother Wallace disappear from the UK after the 1881 census, and it seems pretty conclusive that the Joseph James Cornhill, Baker, who married Ada Rope in Mudgee in 1891 was our man.
Of Ada's children it is likely that at least the last boy, Ernest, b 1887, was a son of Joseph James. When he died in 1927, his parents were named as James J and Ada. His mother Ada is shown on his military records as next of kin, initially as Ada Rope of Mudgee, changed later to Ada Mary Cornhill of Gulgong. The father's name of James J on the death certificate could be coincidence, but given that Joseph James's father was also Joseph, it's quite possible that he was known as James in everyday life. (I myself am known by my second name, as I share my mother's first name.)
So you may have Australian relations much closer than me - if you can track the descendants of Ernest Edward Rope, b 1887 in Mudgee, died in 1927 in Walgett. If Ernest is the son of Joseph James - and I am pretty sure he was - then he was half-brother to Agnes.
Good luck with them!
If you'd like more info on Agnes's Cornhill side I have them back to about 1763 before running into a brick wall.