Here's a copy of how I cycle a QT. Works great and is really fool-proof. Just my preference, but I don't like LR in QT. it will absorb meds and make exact dosing difficult. Algae sheets can substitute for the grazing, and I use PVC fittings for shelter. I just don't like to use anything in QT that can't just be tossed out or sterilized easily. LR is about the only decent way to control nitrate: but that isn't an issue in QT, at least for fish. When I QT corals, or other inverts, nitrates seldom climb to a problem level; but a WC will handle it if needed.
"n regards to Qt cycling; I've done this for years. Get a HOB filter; I really like Aqua-Clear, they have a big sponge and last forever. Don't use the carbon or ceramic noodles that come with the filter. Also, have some extra sponges on hand, they're cheap. Keep a sponge in the flow somewhere in your DT. When you need a QT or HT, just use the sponge that has been in your main system in your QT filter---the QT will be instantly cycled. When done, toss the sponge and keep a new one ready in your main system.
BTW, Cupramine copper, used in a QT,will not destroy a bio-filter."