McQueen was a goalkeeper as a schoolboy but later switched to centre-back. He was signed at the age of 18 by St Mirren. He soon had scouts from other clubs monitoring his progress and it was Leeds United who finally offered £30,000 in the 1972 close season, seeing him as a long-term replacement for the ageing Jack Charlton. Charlton played for some of the 1972–73 season but had decided to retire as the season was drawing to a close. McQueen played on six occasions in his first season at Leeds but missed out on the 1973 FA Cup Final, with manager Don Revie instead opting for the experience of utility player Paul Madeley.