Hey Kevin, like PBK said, there are groups of fresh and marine fish that don't do well with copper treatments. (SW butterflies come to mind). As I recall, our native blennies, skillet fish, gobies should do fine. Couple of things to keep in mind though.
1. Whatever porous/absorptive materials are in your QX tank will absorb copper. (Filter sponges, gravel, rocks, various decor, etc). They will then re-release it slowly back into the system once the treatment has ended. This could play a factor down the road if you add additional species that are much more sensitive to copper--and could die as a result. (With the native species you are keeping, you should be fine. Only relevant if you decide to keep exotics later on and use some of the same equipment from the copper treatment).
2. Ideally, you want to have a dedicated tank and equipment that is only used for copper. Bare bottom, minimal decor. (PVC tubes and elbows used for hides are common, as well as the black, contractors, trash bags cut into longs, thin strips for 'faux plants'. Both work well in this application). Extra air is essential! Add a couple large airstones in addition to whatever filtration is running. O2 levels will drop and stress or kill your fish even if the copper itself doesn't. Elevated respiration rates are expected but keep an eye on the fish, behaviorally speaking. Significantly decreased feeding, poor response to stimulation (gentle knock on the glass doesn't elicit a 'startled' reaction like it commonly would) would indicate that the treatment should be terminated immediately.
3. The general protocol for public aquariums using copper is to SLOWLY add small amounts of copper--testing daily--until the therapeutic/desired level is met. Then maintain that level for 7-10 days. When the treatment is over, multiple large water changes to remove all the copper. There are products which you may or may not be familiar with that can be added to the filtration that will help remove any trace copper leftover. (They are essentially polymer filter pads that change color indicating they have removed heavy metals).
I've never done a Cu treatment at home with the Cupramine purchased from a LFS so I cannot comment on it, or what concentrations you should aim for, directly. It seems to be safe and efficient if the directions are followed and you keep a close eye on your fish.