Gunn was given an appointment in the Royal Engineers at Barbados, but left there in 1829 to go to Van Diemen's Land (now Tasmania), where he obtained the position of superintendent of convict barracks at Hobart Town.
He became assistant police magistrate at Hobart Town in 1838, and in 1839 private secretary to Sir John Franklin and clerk of the executive and legislative councils.
In 1841 he gave up these appointments to take charge of the estates of William Effingham Lawrence, and spent much time investigating the flora of Tasmania.
But his interests were not confined to botany; he became a general scientist and made collections of mammals, birds, reptiles and mollusca, for the British Museum.
accompanied with notes that display remarkable powers of observation, and a facility for seizing important characters in the physiognomy of plants, such as few experienced botanists possess’.
When private secretary to Sir John Franklin he assisted in founding, and was editor of, the Tasmanian Journal of Natural Science, which recorded papers read at government house.