This ad appeared in the papers for about a month:
Argus, Melbourne, 4 Apr 1859,
The Age, Melbourne, 4 Apr, 1859:
Missing Friends.
EDINBURGH.— Alexander Horn and family, from Edinburgh, who arrived in Sydney in 1851,— your brother David's daughter, Jessie, is in Sydney, and anxious to hear from you. Address, Mr. Dickson, London Chartered Bank, Sydney. Any information respecting them will be gratefully received. 1 8108
I don't know if they contacted Jessie, who remained in NSW and married Robert Kirkpatrick in 1863.
I haven't found deaths for either Alexander or his wife, but when daughter Bennet married in 1865 Alexander was no longer alive. Bennet died in 1906 and her brother William in 1908.