Daughter of a Methodist Minister, Sarah Jackson was educated at the Methodist Ladies' College (MLC). She went to the University of Adelaide, graduating with a Bachelor of Arts in 1911 and winning the Tinline Scholarship in English History, then worked on her Honours thesis from home - at first from the Manse at MacLaren Vale, then at Bowden. The subject of her BA thesis was the History of the State 1850-1856. She gained Honours in philosophy (1913) and a Master of Arts (1914). In 1914 she won the David Murray Scholarship for a philosophical essay.
Jackson's parents were happy to support her, but she wanted to be independent, becoming a teacher at MLC and giving lectures in psychology at the Workers' Educational Association in Broken Hill and Adelaide. She had a breakdown in late 1917 - early 1918 and spent a long period in hospital. Jackson then became a tutor in philosophy at the University of Adelaide.
Jackson was an honorary editor of the Women's Record, a paper aiming to keep the various women's organizations in touch with each other, and she wrote short stories, articles and book reviews for a number of magazines and newspapers including the Adelaide University Magazine, Orion, the Red Cross Record and the Women's Record. She was a foundation member of the Women Graduates' Club, and a member of the Womens' Non-Party Association and later of the Social Efficiency Committee. She urged for fully trained workers to be appointed to Minda Home.
Jackson developed tuberculosis and by 1922 was seriously ill. She worked to get a Women's Room at the Kalyra sanatorium, where she was spending much of her time. She hoped to get a psychological clinic established at the University of Adelaide. After her death at the age of 32 in 1923, money was raised in her name in the hope that such a clinic could be established. However, as the amount raised fell short of what was needed, it was spent instead on psychology books for the university. Books in the Barr Smith Library purchased from that fund bear a bookplate identifying them as belonging to the Elizabeth Jackson Library.
A collection of Jackson's papers (mainly letters, loose papers, and a diary in a notebook kept from 1906 to 1918) are kept at the Barr Smith Library.