The paper estimates long run social mobility in Australia 1870 - 2017 tracking the status of rare surnames. The status information includes occupations from electoral rolls 1903-1980, and records of degrees awarded by Melbourne and Sydney universities 1852-2017. Status persistence was strong throughout, with an intergenerational correlation of 0.7-0.8, and no change over time. Notwithstanding egalitarian norms, high immigration and a well-targeted social safety net, Australian long-run social mobility rates are low. Despite evidence on conventional measures that Australia has higher rates of social mobility than the UK or USA (Mendolia and Siminski, 2016), status persistence for surnames is as high as that in England or the USA. Mobility rates are also just as low if we look just at mobility within descendants of UK immigrants, so ethnic effects explain none of the immobility.