Doris Chennells was the daughter of William R. Chennells and his wife Louise Elizabeth. She passed the matriculation examination of the University of the Cape of Good Hope in 1906. She continued her studies at the South African College, Cape Town, in 1908 and was awarded the degree Bachelor of Arts (BA) in Literature and Philosophy by the University of the Cape of Good Hope in 1910. The next year she sent a collection of 80 plant specimens from the Orange Free State (now the Free State) to the South African Museum, Cape Town. Her specimens were of interest because the museum had not yet received many plants from that province.
Chennells resided in Kroonstad for a few years, but returned to Cape Town in 1914 for further studies at the South African College, passing the Teachers' Certificate Examination in 1915. She then became a school teacher in Bulawayo, Southern Rhodesia (now Zimbabwe), where her parents were living. There she became a member of the Rhodesia Scientific Association. Later she married Mark Morisse, a merchant, and settled with him in Johannesburg. He died in 1940 and they had no children. In 1943, while on her way by train from Bulawayo to Johannesburg, Doris bled to death as a result of extensive cancer of the uterus.