Ahem .... convicts were first sent to Australia in 1788, not 1868. Back to the history books for you, Jerry! W.A. can lay claim to be the only State founded by free settlers (1826 for Albany, and 1829 for Perth), and W.A. only had convicts sent here between 1850 and 1868 - therefore only a small percentage of West Aussies, can claim convict ancestry.
My parents arrived as "Ten-Pound Poms", Dad from England in 1925, and Mum from Scotland in 1929. Mum was fond of the old comment, "We arrived as 'Assisted Immigrants', not 'Insisted Immigrants'". 😄