Daughter of Denis and Louisa Trehy, Annie Dodwell came to SA in 1884 and was educated at the Advanced School for Girls. In 1990 she graduated with a Bachelor of Science degree from the University of Adelaide, one of the early women science graduates. She passed third year 1890 with third class honours in Physiology and Geology, and she also had a talent for pure mathematics. She taught geology at the Tsong Gyiaou school at MacLaren Vale.
In 1907 she married George Frederick Dodwell, who held a position at the Adelaide Observatory. In 1909 he was appointed Government Astronomer. Annie also took up the study of astronomy "and as an authority on that science achieved a reputation only second to that of her husband among astronomers in this state" (The Advertiser, Obituary, 7 October 1924, p. 10). Another of her skills was as an amateur photographer.
Annie was also concerned about social and political issues of her time. She was connected with the Cheer-Up Society. She was a member of the League of the Empire, and a recognised authority on Imperial politics. In 1920, with other women graduates, she was appointed by the Girls' Welfare Committee to a deputation seeking increased facilities in domestic training. She died at home in 1924 after a long illness, apparently cancer, and was buried at North Road Cemetery, in plot 6066. Her husband, who was 9 years younger than she was, outlived her by nearly 40 years.