Dunbar began her first play The Arbor in 1977 at the age of 15, writing it as a classroom assignment for CSE English. Encouraged by her Teacher, she was helped to develop the play to performance standard. It was premiered in 1980 at London's Royal Court Theatre, directed by Max Stafford-Clark. Alongside an entry by Lucy Anderson Jones, It jointly won the Young Writers' Festival, and was later extended and performed in New York. The play described the experiences of a pregnant teenager with an abusive drunken father. On 26 March 1980, she was featured in the BBC's Arena arts' documentary series.