I must be missing something since you said you HAVE to take it with you. If you're worried about feeding it, don't...your eel will be fine for a week on its own...just make sure it can't escape.
If for whatever reason you HAVE to travel with the eel, use a 5 gal bucket with a perforated snap-on lid, a battery-operated air pump (just shove a piece of rigid airline into one of the holes in the lid), and a piece of PVC or ABS pipe for the eel to hide in. In fact, I probably wouldn't even feed it at all to keep the water quality up (let it fast a couple of days before you move it too). You'll likely have to replace a gallon of water or so about every-other day with new SW as well.