And keep in mind that letting the water stand for 24 hours will dissipate chlorine, but not chloramines, which are still toxic and need to be removed.
Claire, why don't you just use established media in a new tank? If you move an established filter into a new tank, you don't have to do any waiting for cycling. It's already cycled. Then just put a new filter on the established tank, and it's already cycled too (because of substrate and decorations, etc.).