Born in the Auckland suburb of Saint Heliers on 27 February 1928, Cartier began dancing on stage at the age of four in a pantomime. While studying ballet with Valerie Valeska and Bettina Edwards, she saw the Borovanski Ballet on tour, and decided to make dance her career. In 1946, following in the footsteps of Bettina Edward's student Rowena Jackson, she emigrated to England on scholarship to the Royal Ballet School, studying with Winifred Edwards, George Goncharov, Vera Volkova and Audrey de Vos.