In 2013, Doran almost became the youngest player to score a First Grade century; playing for Fairfield-Liverpool against Sydney University, he was on 87* when his team declared.[4] Aged 16, Doran became the youngest player ever to play for New South Wales second XI.[5][6] For the 2014/15 season, New South Wales signed Doran on a rookie contract,[7] and in October 2014, Doran signed for Big Bash team Sydney Thunder, making him the youngest player to sign a Big Bash contract.[5][8] Doran signed a one-year contract with the Thunder, a week before finishing his HSC exams.[5] Three other teams, including the Melbourne Stars were believed to have been interested in signing Doran; the Stars would have offered him a senior deal.[6] In January 2015, Doran made his BBL debut for Thunder in a Sydney Derby match against Sydney Sixers; Doran did not bat in the match.[9]
In March 2015, Doran signed for Tasmania from New South Wales on a two-year contract.[10][11] He made his first-class debut in a Sheffield Shield match against Western Australia, making scores of 5 and 17.[12] In his first five Sheffield Shield matches, he averaged 19.70, with 2 half-centuries.[13] In September 2015, Doran was added to the Tasmania squad for the Matador Cup, and he made his List A debut a month later against Queensland, but did not bat in the match.[14][15]