Meredith established the Chelsea Book Club in 1932 after graduating from the University of Sydney with a Bachelor of Arts degree. The club's activities included the Chelsea Theatre Group where she encouraged original works by members. Her first full length play Wives Have Their Uses was performed by the Chelsea Theatre Group in 1938. It was later published in 1944 and produced in Sydney, Melbourne, Brisbane and Perth. She also worked in the Independent Theatre as a secretary during this time and had two of her plays produced. In 1939 she contributed to the radio serial Fred and Maggie Everybody.
Her radio play The Opportunist (1940) won the Listener's Choice award in the 1940 ABC Play Competition. This resulted in Meredith being asked to write a new radio serial The Lawsons (1944-1949). It was conceived as rural education outreach for new farming methods for the war effort and thus began her long relationship with the Australian Broadcasting Commission (later Corporation), writing plays, serials and documentaries. The naturalness of her dialogue and characters continued to be her trademark in the sequel Blue Hills (1949-1976), which was more character driven, as it was set in a country town and revolved around a doctor's family. She was a writer on Autumn Affair (1958-1959), Australia's first television continuing drama shown each weekday.
Meredith also wrote two children's radio serials: Mystery Ships (1945) and Anderson's Place (1946). Among her many radio plays were The Labour of Thine Hands (1952) and Mother Moves: a radio sketch . Her stage plays included 'Murders are Messy' (1939), 'The Lawsons' (1950), 'Ten Ways to Get a Man' (1940), 'Ask No Questions' (1940), 'Binney's Back Again: a one act comedy'(1940), 'Shout at the Thunder' (1942), 'These Positions Vacant' (1945) and 'Cornerstone : a three act play' (1956). She was awarded first prize in the ABC Documentary Feature Competition for Great Inheritance which was published as a book. Inns and Outs (1955) was a travelogue written with her husband Ainsworth Harrison.