Dockrell has represented Ireland from U-13 level upwards. In 2009, Dockrell was part of the 2010 U-19 Cricket World Cup Qualifier winning squad. Victory in this tournament allowed Ireland to take part in the 2010 U-19 Cricket World Cup, where Dockrell made his Youth One Day International debut against South Africa U-19s. Dockrell played a further three Youth One Day Internationals in the tournament.
Dockrell made his debut for Ireland A in 2008. The same year he was invited to coaching sessions with Somerset County Cricket Club.
Somerset County Cricket Club were interested in Dockrell since he was 15. On 18 July 2010 it was announced that Somerset had offered Dockrell a two-year contract. Speaking of his aims, Dockrell said "My ambitions are to keep making progress with Ireland, but also to get into a county first team by developing all aspects of my game". Commitment to Ireland's internationals in the Intercontinental Cup limited Dockrell's availability for Somerset towards the end of the 2010 season. He was selected in Ireland's 15-man squad for the 2011 World Cup. During the tournament Dockrell suffered a dislocated shoulder. The rehabilitation period meant he missed much of his first season with Somerset. He featured in a single County Championship match, although his appearances in limited overs games were more frequent, playing in the semi-final of the twenty20 cup and the Champions Trophy.
A side made up of some of the best players from Associate and Affiliate teams was put together to face England in Dubai in January 2012. The three-day match was part of England's preparation for a series against Pakistan later that month. Dockrell was one of four Ireland players included in the 12-man squad. Fellow left-arm spinner Murali Kartik left Somerset at the end of the season, giving Dockrell the opportunity to establish himself in the team. In Somerset's opening match of the 2012 County Championship Dockrell took 6/27 in the second innings against Middlesex to help his side to a six-wicket victory.