Upon returning from war, Brooks made his first-class debut for the Royal Navy against Cambridge University in 1919 as a right-handed batsman who bowled right-arm medium. The same season he made his debut for Hampshire against Surrey in the County Championship. Brooks represented Hampshire eight times in the 1919, making his maiden first-class century against Gloucestershire with a score of 107. Brooks represented Hampshire in nine first-class matches between 1919 and 1921, with his final first-class appearance for the county coming against Middlesex. He scored 244 runs for Hampshire at a batting average of 16.26, with one century and one half century and a high score of 107. In 1920 Brooks made his second first-class century, this time for the Royal Navy against the Army, which gave him his highest first-class score of 143. He played as an all-rounder for the Royal Navy, a role he did not fill at Hampshire. In all, Brooks represented the Royal Navy in sixteen first-class matches, with his final appearance for them coming against the Royal Air Force in 1929. In his sixteen matches for the Royal Navy, Brooks scored 690 runs at a batting average of 23.00, with one century and two half centuries and a highest score of 143. With the ball he took 38 wickets at a bowling average of 27.63, with one five wicket haul which gave him his career best figures of 8/90. Additionally, Brooks represented the Combined Services with four first-class matches.
Brooks was appointed Governor of Victoria by PremierThomas Hollway and served from 1949 to 1963. During his term as governor, he acted as Administrator of the Commonwealth three times. He served in this capacity for almost seven months after the governor-general, Viscount Dunrossil, suddenly died in office in 1961 after serving only one year. Sir Dallas was in effect Acting governor-general until the appointment of the Viscount De L'Isle. Brooks served the state for over 13 years, becoming Victoria's longest-serving governor. After his term ended in 1963, he chose to remain in Australia in retirement. He built a house in Frankston and died there three years later.
Freemasonry
Brooks was Grand Master of the United Grand Lodge of Victoria from 1951–1963. He was Victoria's longest serving Grand Master, and he is the only governor of any Australian state initiated to the craft while serving as governor. Brooks had expressed a desire to become a freemason while in England but he had also stated that he preferred to become initiated in Australia. He met with the Grand Master of Victoria and notified him. He was initiated in the Clarke Lodge No. 98 on 6 February 1950 and was passed and raised within two months. He became Worshipful Master of the Lodge only five months after his initiation and he was elected Grand Master of the Grand Lodge of Victoria the following year.
