After graduation, O'Reilly applied for a residency at Sydney University in 1905, whereupon she was rejected in favour of five men. Two of these had come first and second, respectively, in their graduating year, but the other three had received only pass degrees in comparison with O'Reilly's top four placing and honours degree. Women were first admitted to the
Sydney Medical School (founded in 1856) in 1885, and the first females graduated in 1893. Reports from the time suggest that this attitude was in contrast to favourable opportunities to study medicine, where no distinctions in teaching were made between the sexes at the Sydney Medical School. O'Reilly's rejection became the focus of media attention and public debate in the form of editorials and letters to the newspapers about the discrimination and roles of female doctors. She also co-founded the Old Girls' Union at her school MLC Burwood, serving as its president; was a medical adviser to the
Presbyterian Ladies' College, Pymble, and the Kindergarten Training College, Waverley, and a foundation member of the
National Trust of Australia. ==Personal life==