She attended Girton College, Cambridge and took the Natural Sciences Tripos in 1922.
She became a research assistant upon graduation to Edgar Adrian, studying nerve and muscle physiology, before receiving her Ph.D in 1927. Cooper then became a research student and then a research fellow at St Hilda's College, Oxford with the physiologist Charles Scott Sherrington while working as a demonstrator in anatomy for the University of Oxford.
Able to afford household help, she took an unpaid position as a lecturer in natural science at St. Hilda's in 1940 and received a paid position as a research fellow there in 1946 that she maintained until her retirement in 1968.
As an excellent histologist, Cooper fixed, stained, and examined the microstructure of the sense organs.
Alone and with colleagues, she made advances in understanding how the muscle spindles functioned relative to their structure.