Yes, make a copy of your passport. Actually, some people recommend walking around with this -- keep the real one in the safe on the ship. You only need your drivers license and KTTW card to come on and off the ship. When in port, I bring my drivers license and a copy of my passport. If I lost the copy, I still have the original. (Or, if my purse was stolen)
My sister had her passport stolen the day before her flight was to leave. It would have been MUCH easier if she were carrying the copy.