John M. Dunn was educated at the North Adelaide Grammar School, and during his juvenile years also studied piano and sang in the St Peter's Cathedral choir (often in solo parts). He worked for several years in a bank then sailed to London in 1888 to further his musical studies. On his return to Adelaide he taught at the Adelaide College of Music (later Elder Conservatorium) and in 1891 was appointed organist to St Peter's Cathedral. He retained this position for 45 years.
Dunn also served as conductor for the Adelaide Orpheus Society and president of the Adelaide Society of Organists. In 1896 he and and Harry Congreve Evans collaborated on the comic opera The Mandarin. It was staged at Adelaide's Theatre Royal in November that year.