Buday graduated from the National Institute for Dramatic Art in 1983, and has since become one of Australia's leading theatre actresses.
She has performed with most theatre companies, including roles in A Midsummer Night's Dream, Three Sisters, The Importance of Being Earnest, and A Doll's House.
Buday is also a singer, and she has portrayed the lead roles in My Fair Lady, Cabaret, High Society, and The Threepenny Opera.
She made her major screen debut as Savannah Nix, leader of the feral children, in Mad Max Beyond Thunderdome.
Besides her regular theatre work, she has also appeared in various television series including Land of Hope, Secrets, Water Rats, and Stingers.