If you're treating with copper, it sounds more like a hospital tank than a QT. The copper has ruined the rock you put in there. It will have killed all the bacteria and permeated the rock, so don't ever put it back in the DT. Its a table decoration now. Better yet, throw it in the garbage so you don't accidentally put it in the DT.
A hospital tank is for treatment and medications. Nothing goes in there except some pieces of PVC
pipe for hidey holes. Medications will kill the bacteria that process waste, so frequent water changes are required. If you go with hyposalinity instead of copper treatments, you could put stuff back in the DT/sump as it is not contaminated, but that horse is out of the barn.
A QT is just a place to observe a fish to see if it is sick. LR
from your tank/sump can go in their along with bio filter pads (I always keep my filter pad for my QT in the sump when not in use) and then back into the DT/sump afterwards. BB can build up and process waste, keeping ammonia low or 0.
Your hospital tank with copper treatments will require water changes. A lot! keep an eye on ammonia and keep lots of water on hand.