Hi Shirley
My Dunn line goes back to my 5th GGF, Archibald Dunn of Liberton, Edinburgh - 1743-1792
One of Archibald's sons was called Robert - b1786 - he married Janet Inglis and they had at least 8 children, all born in Liberton between 1807 and 1829
One of those children was Ann Dunn - b 2nd July 1826
I have no information other than births / christenings
It's possible that Robert, wife Janet and all 8 kids went to Australia (or anywhere else) - they seem to disappear from UK records
it seems unlikely that an unmarried Ann would have travelled by herself
Do you have any other clues - Ann's brothers / sisters were
Janet, James, Isabella, Sarah, Jean, Robert, Ann, Margaret