Moya was educated (1917–27) at Firbank Church of England Girls' Grammar School, Brighton.
After visiting Paris in 1928, she studied at the National Gallery of Victoria Art School, Melbourne, from 1929 to 1932 where she met her future husband Sam Atyeo.
After NGV, Moya studied under George Bell in the Bourke Street Studio School in Melbourne.
He and Sam Atyeo encouraged her to experiment with modernism.
Sunday Reed also studied at Bell's School at the time.
For several months in 1937 she took charge of Heide, the home and garden of the art patrons John and Sunday Reed, at Bulleen, a suburb of Melbourne.
Dyring's husband, Sam Atyeo, had an affair with Sunday Reed and later Dyring had an affair with Sunday's husband John.
She had a successful solo exhibition at Riddell Gallery in Melbourne in June 1937.
In August 1937, Dyring embarked for Panama, then travelled to New York.
She disliked the work of contemporary American artists and sailed for France.
In 1938 she was based in Paris, taking advantage of Atyeo's contacts within the avant-garde.
Atyeo accepted a commission in Dominica, and left Dyring in Vence.
At the outbreak of war she was evacuated back to Australia.
She travelled to Dominica where she married Atyeo.
However, they were not happy and divorced in 1950.
She returned to Australia every three years until 1963.
Two of her earliest works, Melanctha, 1934, a small cubist work, and Portrait of Sunday Reed, 1934, are part of the permanent collection at the Heide Museum of Modern Art.
She is also represented in the National Gallery of Australia, Canberra.