just using water from a cycled tank will do almost nothing for you. what you really need is a physical surface for the de-nitrifying bacteria to live on. in your main tank that physical surface is your rock and your filter media.
i will assume your QT is bare bottom, with some pvc
fittings for fish to hide in, and a basic HOB
filter. if that is the case, you NEED to ensure that your filter media is colonized with de-nitrifying bacteria BEFORE you add your fish to the QT. The way to do this is to either keep a filter cartridge in the main tank (or sump) and pull it out when you need to do your QT.... or to provide some live rock or something in your QT.
if you cant keep a QT filter cartridge in your main tank or sump then you can cycle your QT the same as your main tank, and after the cycle is done, you will need to "feed" your QT to maintain some ammonia and nitrite for the bacteria. feeding your QT can be as simple as tossing in a few flakes of food a couple times a week... just something to decay and feed the bacteria.
Keep in mind that if you put live rock in your QT, and then you medicate your QT, you can never put that live rock back into the main tank, as it may leach copper into your tank from the medication (killing your inverts).