Not to be the bearer of bad news, but i think you should reconsider that zebra moray eel as well. That thing gets to be 5 feet long. Not really a great choice for a 55G tank. As for the ich/eel thing, the eels are fairly resistant, but they CAN be infected by the cryptocaryon parasite, so yes, you need to get him out of there ASAP, and he needs to be treated. As far as the treatment, I can't help you with that because i have no experience in that department. You should open up a thread in this sub-forum Saltwater & Reef - Sick Fish or Coral - Aquarium Advice - Aquarium Forum Community
and state the fact that your eel most likely has ich. I'm not sure if copper treatments are safe for eels, so make sure you ask first before you decide to do anything. My guess is everyone is going to tell you to utilize the hyposalinity method of eradicating the ich parasite.
Another thing.. how big is your eel currently? The current size is going to determine how large of a QT tank you will need.
As for the QT, i don't believe your carbon pad will do much. Do you have any bio-balls or ceramic media filter in that canister? You need to use media other then that carbon.
Do you even have a protein skimmer on your 55G? Those are two pretty messy fish with huge bioloads.
And again, not to be mean, but we could have guessed this would have happened. You have two fish, that need tanks larger then 100 gallons, and that have huge bioloads, and are probably stressing eachother out. 2.5 inches isn't very big, and i'm sure that eel is always looking for it's next meal.
Regardless, it would be a ton more helpful for us if you gave us LOTS more details about your system. What equipment you have running on it, ALL of the inhabitants, and how long you've had this system running. And basically anything else you can think of that you may find important.