Robert Brodie, the only son of the late Malcolm Brodie who had come from Glasgow to Melbourne, was born in Melbourne on 23 January 1898. His mother died when he was born and he was brought up by an aunt. At an early age he went to Glasgow and remained there until 1910. His early education was taken at Kelvingside Academy, and after his return to Australia he was a boarder at Geelong College. He always had a limp because in childhood he had fallen from a horse and broken his left thigh and he was one of the first, if not the first, treated by the Hamilton Russell method. He volunteered for active service with the First Australian Imperial Force (AIF), but was rejected because of this injury.
He graduated MB BS from the University of Melbourne in 1921. His clinical instruction was obtained at the Alfred Hospital, where for many years his father occupied a prominent position on the board of management.
After experience as a resident medical officer at Ipswich, Queensland, he travelled to England and was house physician and house surgeon at St George's Hospital, London in 1922 and 1923. After further study in Edinburgh, he obtained the Fellowship of the Royal College of Surgeons of Edinburgh. He then pursued postgraduate studies in dermatology in Vienna before returning to Melbourne. Shortly afterwards, he entered private practice in dermatology in association with Dr Herman Lawrence, and was appointed clinical assistant to the dermatological clinic at the Alfred Hospital where he was assistant dermatologist to SW Shields from 1927 to 1947, and honorary dermatologist from 1948 to 1952. He was honorary consultant dermatologist to the Victorian Eye and Ear Hospital from 1928 to 1955. In 1939, he was admitted a Member of The Royal Australasian College of Physicians, and was elected to Fellowship in 1947.
In 1941, he joined the Second AIF as a specialist dermatologist to 2/7 Australian General Hospital. He served in the Middle East, later in Queensland, and in New Guinea and Borneo. He resumed practice in 1946, and continued active work in his profession until a few weeks before his untimely death.
Robert Brodie was active in the foundation of the Dermatological Association of Australia and became the second president. He loved his weekly game of golf and was an avid reader. His great absorbing hobby was trains – miniature and real. His knowledge of the world's trains was extraordinary, and journals on trains both local and overseas arrived regularly. He stuck meticulously to the metric system and it irritated him to see a prescription made out with a mixture of the metric and standard systems. Even in his private life he favoured the metric system.
Robert Brodie, apart from being a remarkably able dermatologist, was a true physician, concerned not only with his patient's complaint but with all aspects of his patient's welfare. He was an extraordinarily kind and generous person. He died of aplastic anaemia on 10 February 1960, in Melbourne at the age of 62.