The Light Blues made their way into the last eight with a 1-0 win over Falkirk last night and now they will meet the Dumfries side at Ibrox for a place in the semi-finals.
The tie is due to be played on Sunday, September 9 but this falls during an international period and the game is almost certain to be switched.
It is understood the dates of September 18 or 19 are being looked at and we will confirm this as soon as possible.
The two sides last met in competitive action in the League Cup at Palmerston on September 25, 2009 when Rangers won 2-1. Neil Alexander and Lee McCulloch are the only survivors from that night.
Of course, Rangers also beat Queens 3-2 in the 2008 Scottish Cup Final.