If you treat your q-tank with copper, which is an effective medicine/poison for the parasites, you will also severely disrupt the bio-filter by killing most of the bacteria in the filter, plus you're killing any micro-life in the water, which means more dead stuff and hence decomposition. This is the dilemma with q-tanks, expecially small ones.

You'd probably be better off trying this approach, although it's a PITA. First, set up your q-tank with new water, and for filtration, you can use a little hang on filter with bio-balls or chem stars and an airstone in the chamber. You can cycle this with either ammonia sulfate (I think, but could be wrong) or something like a rotting shrimp, i guess. Adding ammonia works great. The idea is to build up a large colony of bacteria in the bio-balls residing in the filter chamber. Then, when you add sick fish and copper, some of the bacteria in the filter survives, plus there's less stuff in the water killed by the copper. This should help to keep ammonia levels down.

At the old AQSS, they quarantined fish with copper in a big system in the back room. Basically Ken told me that the bio-filter in that sysem had acclimated to the presence of copper somewhat, so they were able to keep copper up and ammonia down.