Dunne began his military service with the Territorial Force of the New Zealand Army in 1971. He was transferred to the Regular Force in October 1977 at the rank of lieutenant, in the Royal New Zealand Infantry Regiment. He was posted to 1 Ranger Squadron, New Zealand Special Air Service, Papakura, and employed as a troop commander. As captain, he was deployed overseas with the New Zealand Army Truce Monitoring Contingent in South Rhodesia. In July 1989, Dunne was appointed commandant of the Officer Cadet School in Waiouru and promoted to lieutenant colonel. In September 1999 he was deployed with the New Zealand Force East Timor as the senior national officer. He was promoted to brigadier in October 1999 and commanded Dili Command, an operational formation in the International Force East Timor (INTERFET). In that capacity in East Timor, Dunne commanded New Zealand Forces and international troops during New Zealand's largest deployment since World War II. He was promoted to the rank of major general on 2 April 2001 prior to assuming his appointment as Commander Joint Forces New Zealand (COMJFNZ), which post he held until 2004.