McQueen joined the Rabbitohs in 2009 and spent the majority of the season playing for the Rabbitohs feeder team, the North Sydney Bears in the New South Wales Cup competition. He made his NRL debut in Round 22 of the 2009 season, days after his 22nd birthday. A late call up to the side, McQueen played on the wing and scored a try in South Sydney's 36–22 win over the Manly Sea Eagles. Due to injury, McQueen missed the entire 2010 season. He returned to first grade in 2011, playing almost every game for the Rabbitohs, switching between wing and second row, and was named in Australia's 34-man Four Nations train on squad. Later that year he represented the Prime Minister's XIII against Papua New Guinea. In 2012, he began the season again at wing, before making a permanent switch to second row. In 2013, McQueen cemented his spot in the South Sydney starting side. In 2012 and 2013, he was a member of Queensland's Emerging Origin Squad. In 2013, he made his State of Origin debut for Queensland. He played all three games of the 2013 State of Origin series in which Queensland extended their record for consecutive series victories to eight. On 5 October 2014, McQueen was selected to play for the Rabbitohs from the interchange bench in the 2014 NRL Grand final, helping them to a 30–6 victory over the Canterbury-Bankstown Bulldogs. On 26 September 2015, McQueen again played for the Prime Minister's XIII against Papua New Guinea.
Gold Coast Titans
On 11 December 2015, McQueen signed a 2-year contract with the Gold Coast Titans starting in 2016, after being released from the final year of his Rabbitohs contract.
Wests Tigers
On 12 April 2017, it was announced that McQueen would join the Wests Tigers on a three-year deal, starting in 2018. McQueen started off the 2018 season playing for Intrust Super Premiership NSW side Western Suburbs after being unable to break into the starting 17 for The Tigers. After spending the first 10 games in reserve grade, McQueen was called up to The NRL side for their Round 11 clash against Penrith. McQueen was limited to only 6 games for the Wests Tigers in the 2019 NRL season. McQueen instead spent most of the year playing for Western Suburbs in the Canterbury Cup NSW competition.
England
McQueen was called up to the England national team by coach Wayne Bennett for the test against Samoa on 6 May 2017. It was the first time that McQueen had accepted England after rejecting an approach for the 2013 World Cup in order to play for Queensland in the State of Origin. The Brisbane-born player qualifies for England through his father.