As luck would have it, I returned to work the day you replied previous to which I had five weeks off to look into such things. I am working all weekend.
My great grandmother is the Tasmanian connection. She is Amy Louisa Moody born 1888 (birth registered as Annie) and her parents were James Moody born 1836 and Elizabeth Jane Johns born 1848. To have a DNA cousin relationship you have to have a common direct ancestor/s at some point. To me this does not fit with Nicholas and his own age or arrival in Hobart. I realise as a mariner that he could have been here before, but possibly not.
It is mainly four DNA matches to the same people on Ancestry to myself, my mother, my maternal aunt and her daughter. Apart from my cousin, we are all also on My Heritage. There is a shared match on Ancestry with another descendant of James Moody and Elizabeth Jane Johns. also, the person I have exchanged results with has one other Moody match to the next Moody generation back. also, a shared match to someone in Canada, who added Bonnitcha after I emailed, but actually has no known connection!
My other aunt, her first cousin, cousins two children and granddaughter do not get the DNA matches.
