Kelly's maternal grandfather was an Argentine-born, Italian-speaking opera singer, Count Ercole Filippini, a leading baritone for the La Scala Opera Company in Milan. Filippini was touring Australia in 1914 with a Spanish opera company when World War I broke out; Filippini stayed and later married Anne McPharland, one of his students. As Countessa Anne Filippini, she was Australia's first female symphony orchestra conductor. She sang the role of Marguerite in Australian Broadcasting Corporation (ABC) Radio Perth's performance of "Faust" in 1928. Kelly's grandparents started the Italo-Australian Opera Company, which toured the country in the 1920s.