[1][2] Molony's long academic career with the ANU began in 1964, when he was employed as a research assistant in medieval history in the school of social science.
Following his retirement from the ANU in 1990, Molony was appointed to the Keith Cameron Professorship of Australian History at University College Dublin.
In 1993, on his return to Australia, Molony was appointed to the Foundation Research Professorship in History at the Australian Catholic University in Canberra.
During the course of his career, Molony published a number of scholarly works on subjects as diverse as the encyclical of Pope Leo XIII and Ned Kelly to the bicentennial history of Australia, as well as numerous newspaper and journal articles, chapters in books and literary reviews.
[3] Out of all of his published works, Molony said that he believed his 2000 book, The Native-Born: The First White Australians, would be judged as his most significant original contribution to the writing of Australian history, stating: "I say this because the native-born had never been given the serious consideration they deserve for their contribution to the making of our nation.