It appears Alexander may have headed to Victoria after gold during the 1850s, as did many South Australians. The first gold to be found in Victoria was in 1851.
There is an unclaimed letter addressed to Alexander Barreau which was ‘lying at the Post Office at Forest Creek’, according to the Victorian Government Gazette, June, 1852, p.874. Forest Creek is modern day Castlemaine.
He must not have stayed for too long as his wife (Elizabeth Hamilton) another child in June 1853.
Government Gazette, Victoria. Online Archive, 1836 – 1997, State Library of Victoria, http://gazette.slv.vic.gov.au/, June 1852, Gazette 33, p. 874.