Dobbie moved to Swansea City in 2009. Dobbie was loaned to Blackpool and won promotion to the Premier League, winning the 2010 play-offs. Dobbie returned to Swansea City and again won promotion to the Premier League via the 2011 play-offs. Dobbie was again loaned to Blackpool in 2012 and played in a third successive play-off final, this time as a runner-up. In 2012 he signed for Brighton & Hove Albion before joining Crystal Palace, initially on loan, where he helped the "Eagles" to win promotion in 2013 to the Premier League (but on this occasion was not part of their play-off winning team).