Technically Quartermaster referrs to the individual, not the location. Wikipedia's entry on "Quartermaster" states that...
"In the British Army, the Quartermaster (QM) is the officer in a battalion or regiment responsible for supply. By longstanding tradition, he or she is always commissioned from the ranks (and is usually a former Regimental Sergeant Major) and holds the rank of captain or major. Some units also have a Technical Quartermaster, who is in charge of technical stores. The Quartermaster is assisted by the Regimental Quartermaster Sergeant (RQMS) and a staff of storemen. The QM, RQMS and storemen are drawn from the regiment or corps in which they work, not from the Royal Logistic Corps, which is responsible for issuing and transporting supplies to them."
Obviously things changed a bit when the tradition was taken up in Canada, but the concept is the same. By convenience, the QM's Stores are shortened to QM, so this is how we have a QM run by a QM.
*edit* A simpler way of looking at it is that the QM is the place you're most likely to find the QM. */edit*
