You need a valid passport. If it is not a British passport you will also need to check if you need a visa for Eire. I know someone who was refused boarding for this very same cruise back in May as she was Thai and did not have a visa for Eire.
I think you will find that because RCI run on American principles you will need a passport, it's not like a RORO ferry and there are security measures in place which insist on you having a passport. To get a definitive answer ask RCI.... Neil.