Dunlop was born in Major Plains, Victoria, the second of two children of parents James and Alice. He attended Benalla High School for two years of his education. He started an apprenticeship in pharmacy when he finished school, and moved to Melbourne in 1927. There, he studied at the Victorian College of Pharmacy and then the University of Melbourne, where he obtained a scholarship in Medicine. Dunlop graduated from the University of Melbourne in 1934 with first class honours in pharmacy and in Medicine, and excelled as a sportsman at Melbourne University and Ormond College. The nickname "Weary" was a reference to his last name—"tired" like a Dunlop tyre.
Dunlop had been a school cadet, and he continued his part-time army Service until 1929, when his Service ceased under pressure from his pharmacy studies. He re-enlisted in 1935 and was commissioned into the Australian Army Medical Corps on 1 July with the rank of Captain. In May 1938 Dunlop left Australia for London on a ship, where he served as her medical officer. In London he attended St Bartholomew's Medical School and in 1938 became a Fellow of the Royal College of Surgeons. The distinguished medical mentors Dunlop met in London, Professor Grey-Turner and Sir Thomas Dunhill, impressed him with their dedication to their job and he resolved to emulate their Example.
While at university Dunlop took up rugby union commencing as a fourth grade player with the Melbourne University Rugby Club in 1931. He rapidly progressed through the grades, to state and then to the national representative level, becoming the first Victorian-born player to represent the Wallabies.
He made his national representative debut against the All Blacks at the Sydney Cricket Ground on 23 July 1932 as a number 8.
In the first Test of 1934 he again appeared for Australia, this time as a lock. Australia won the match 25–11, and two weeks later the second and final match of that year's Bledisloe Cup series finished in a draw. Although Dunlop missed that match due to injury he stands as a member of the first Wallaby squad to have won the Bledisloe Cup away from New Zealand.
During World War II, Dunlop was appointed to medical headquarters in the Middle East, where he developed the mobile surgical unit. In Greece he liaised with forward medical units and Allied headquarters, and at Tobruk he was a surgeon until the Australian Divisions were withdrawn for home defence. His troopship was diverted to Java in an ill-planned attempt to bolster the defences there. On 26 February 1942, he was promoted to temporary lieutenant-colonel. Dunlop became a Japanese prisoner of war in 1942 when he was captured in Bandung, Java, together with the hospital he was commanding.
Because of his leadership skills, he was placed in charge of prisoner-of-war camps in Java, and was later transferred briefly to Changi, and in January 1943 commanded the first Australians sent to work on the Thai segment of the Burma-Thailand railway where prisoners of the Japanese were being used as forced labourers to construct a strategically important supply route between Bangkok and Rangoon. Conditions in the railway camps were primitive and horrific—food was totally inadequate, beatings were frequent and severe, there were no medical supplies, tropical diseases were rampant, and the Japanese required a level of productivity that would have been difficult for fully fit and properly equipped men to achieve.
After 1945, with the darkness of the war years behind him, Dunlop forgave his captors and turned his energies to the task of healing and building. He was to state later that " in suffering we are all equal". He devoted himself to the health and welfare of former prisoners-of-war and their families, and worked to promote better relations between Australia and Asia.
In 1988 'Weary' Dunlop was named one of '200 Great Australians'. In June 2008, he was honoured in the third set of inductees into the Australian Rugby Union Hall of Fame.
He received the posthumous honour of having the Canberra suburb of Dunlop named after him shortly after his death in 1993. His image is on the 1995 issue Australian fifty cent piece with the words "They Served Their Country in World War II, 1939 – 1945". The fifty cent piece is part of a set including the one dollar coin and the twenty cent piece. He has a platoon named after him in the Army Recruit Training Centre, Blamey Barracks, Kapooka. Weary Dunlop Platoon is a holding platoon to recruits that want to leave recruit training.
He was on one of 1995 Australia Remembers 45c stamps.
In June 2008, he was honoured in the third set of inductees into the Australian Rugby Union Hall of Fame. To date, he is the only Victorian so honoured.