After Tuesday night's 1-0 victory over Stranraer at the National Stadium, Queen's will travel to Firs Park to take on Third Division side East Stirlingshire.
"Shirey" advanced into the draw with a fine 4-2 victory over fellow basement league outfit Dumbarton in Falkirk this midweek and will prove a tough proposition for Billy Stark's side on the perrenially awful park at Firs.
Queen's travel to Falkirk for the third time in cup duty in the last three consecutive seasons, on either September 4th or 5th.
The full draw is as follows:
Airdrie United -vs- Arbroath
East Stirlingshire -vs- Queen's Park
Montrose -vs- Brechin City
Peterhead -vs- Morton
Ross County -vs- St Johnstone
Partick Thistle -vs- Berwick Rangers
Clyde -vs- Dunfermline Athletic
Forfar Athletic -vs- Ayr United