I would recommend removing everything from your filter as it is not cycled. You most certainly do not want your QT to go through a cycle whilst treating your sick and stressed fish.
I would also recommend ditching the copper and going with hyposalinity as you don't have to keep replacing the medication every time you do a water change. It only takes one mistake to overdose on copper!
You may need to do daily water changes to keep your water stable but do what is necessary. You won't regret it in the long run.
After you've treated for ich and have allowed your tank to go fallow for 6-8 weeks and your fish are back in the DT then I would recommend putting all of your filter media back into the filter of you QT and cycle it. Cycle it well so you know it's ready for any new fish. Treat all new ish with hyposalinity whether they have ich or not as sometimes you just can't see it. Most people would recommend treating for worms and infections which can be used in conjunction with hypo. It cannot with copper!
Current tank 260g FOWLR.
Fish: Moorish Idol, Powder Blue Tang, Hippo Tang, J Emperor Angel, 3 Chromis, 2 Black & White Clowns, Yellow Tang,