Could you hit us with some numbers instead of just saying the parameters are fine? Could you post a picture of the problem?
The QT does not need to be overly fancy. You'll need:

An aquarium or other container large enough to house your largest fish. Aquariums have the advantages of being clear for easier observation of the sick fish, and being the right width for hang-on tank equiptment. Other container types can be used in a financial pinch.

A filter of any type. I personally recommend a cheap sponge filter for this purpose. It is cheap, easy to set up, and areates the water really well. Areation can be important for some types of treatment. Whatever filter you choose, the carbon should be removed during any medicated treatment.

A heater.

Optional: Hood and light. If your fish is a jumper, some sort of covering is needed, but you don't need anything fancy here. The light will make fish observation easier, but a desk lamp will suit just as well as a regular aquarium light.

Optional:
PVC pipe sections large enough for your fish to hide in. Some fish feel much more secure in hiding.

Recommended for saltwater: A separate container to pre-mix a large amount of saltwater in, in case emergency water changes are needed. In a QT tank that has not been cycled, you may have to do frequent 50% water changes to keep the ammonia levels down.
I'm not really the expert here, but I suspect a bacterial infection. It could also be an injury, in which case antibiotics will help prevent a secondary infection while the injury heals.
Is it getting worse at this point, staying the same, or getting better?