Cockburn played for the Australia women's national basketball team at the 1957 World Championship held in Brazil. She was only 16 years-old when she travelled with the team to compete in the Championship. Cockburn was captain of the South Australian junior school girls team which won the Australian trophy in 1954. She was named to the All-Australian schoolgirls team the same year. At 13 years-old, Cockburn was already playing top grade women's basketball in Adelaide.