Hi can someone please help or explain to me how I go about searching for records from Galway from Australia?

I am looking for ANTHONY BLAKE born about 1822 married CATHERINE LINSKY they had two children Harriett Maria b 1858 and Peter b 1861.

Anthony immigrated to Australia in about 1862-3 and Catherine and the children followed in about 1864. Unfortunately I have no other dates.

I would appreciate any help as I think I have made a crack in the brick wall!