Dobbie debuted for the "Hibees" on 9 August 2003 as an 85th-minute substitute in a 2–1 win over Dundee United at Tannadice. After five substitute appearances, Dobbie had his first start on 23 September 2003, scoring a hat-trick in a 9–0 win over Montrose in the second round of the 2003–04 Scottish League Cup. Dobbie's league debut arrived four days later in a 2–1 defeat to Celtic at Easter Road and scored his first league goal on 7 December 2003 in a 3–1 defeat to Aberdeen at Pittodrie Stadium.