The Full Form of QRT is Quick Reaction Task.

In military science nomenclature, a quick reaction force (QRF) is an armed military unit capable of rapidly responding to developing situations, typically to assist allied units in need of such assistance. They are to have equipment ready to respond to any type of emergency, typically within ten minutes or less but that is based on unit standard operating procedures (SOPs). Army cavalry units are frequently postured as quick reaction forces, with a main mission of security and reconnaissance. They are generally platoon-sized in the U.S. military’s combat arms.