If you where already treating a fish for ich, it is most likely (but not 100%) that the goby will have this as well. In fact, the other fish in the main tank will also succumb eventually. If the goby has alot of "fuzzy" patchs, it may be a secondary infection braught on by the parasite and may need treating with a gram negative anti-biotic. I would wait a few days to see what affect the copper treatment has but if it does not show improvement, I would add the anti-biotic.
If the anti-biotic is needed, watch the NH3
levels as the bio filter in the QT will also crash. Water changes will be your only recourse.
As far as the main tank is concerned, there is no effective treatment that can really be recommended to ensure the parasite is eliminated properly other than leaving it fallow for 4 weeks. The best option is still setting up additional housing and QT the other fish.