Harwood was born on 8 June 1920 in Taringa, a suburb of Brisbane. She attended Brisbane Girls Grammar School and was an organist at All Saints' Church when she was young. She completed a music teacher's diploma, and also worked as a typist at the War Damage Commission from 1942. Early in her life, she developed an interest in literature, philosophy and music.[1]
She married linguist Bill Harwood in September 1945, shortly after which they moved to Oyster Cove south of Hobart as he was appointed a lecturer at the University of Tasmania. Here she developed her lifelong interest in the work of philosopher Ludwig Wittgenstein "which informs her entire opus".[4]
Her father played piano, violin, guitar and the flute. Both Gwen and her brother were given piano lessons, and originally Gwen wanted to be a musician. Gwen's grandmother introduced her to poetry; this inspired her and became her lifelong calling and passion.