I keep my emergency QT in a cuoboard. Its never cycled. Yes, i fill it with water from the main tank (more so the fish goes into same water parameters) rinse some sponges into the water and transfer some filter media from main tank into the QT filter to get some bacteria into the filter.
Its not so important to have a cycled emergency QT as it should be low bioload and you do water changes to manage water parameters.
Video on how to set up an emergency QT