She was born with sacral agenesis. Rainbow-Cooper began wheelchair racing in 2013 and is since 2023 coached by the Dutch coach Arno Mul. From 2013 to 2023 she was a part of Weir Archer Academy.[3] In the 2022 Commonwealth Games, she won a silver medal in the marathon (T54) event.[4] She went on to come first in London's Big Half, equalling Manuela Schär’s course record for the women's wheelchair race.[5] In September 2022, she won the women's wheelchair race in the Great North Run.[6] In April 2024, she won the women's wheelchair race in the Boston Marathon, becoming the first woman from Great Britain to do so.[7][8]
Eden made her Paralympic debut at the 2024 Summer Paralympics held in Paris, France.[9] There she competed in the 1500m, 5000m and marathon in the T54 classification. She came 7th in 1500m but failed to finish the 5000m or marathon.[10]