The Australian-born Noonan was encouraged by his father to pursue his interest in film as a teenager. He made his first film, "Could It Happen Here?" (1969), when he was 16. It went on to win a prize for short films at the Sidney Film Festival and later aired on Australian TV. Noonan was one of twelve students (along with Gillian Armstrong and Phillip Noyce) in the inaugural directing program at the Australian Film and Television School in 1973.
Following graduation, Noonan spent five years making documentaries and short films for Film Australia. His "Stepping Out" (1980), a film portrait of a theater troupe of mentally handicapped actors, won praise and brought Noonan to the attention of producer-director George Miller (of "Mad Max" fame). Invited by Miller to join a workshop of actors and directors, Noonan went on to direct the Australian TV miniseries "The Chowra Breakout" in 1985. He subsequently wrote and directed five episodes of the TV miniseries "Vietnam" (1987) and made his Australian TV-movie directorial debut with "The Riddle of the Stinson" (1988). Noonan made his feature film directing debut with "Babe" (1995), the charming fantasy about a pig who learns to be a sheep dog.