Having lost multiple driver's licenses, I feel your pain. I keep my license in a compartment in my phone wallet and when my kids were little, they would play with my phone and pull the cards out. I bet that in this circumstance a picture of the old one along with the new paper one will work in the event your other one does not arrive. I have been allowed to pick up controlled substances before with just a picture of my driver's license and this is nowhere near as serious as that...I mean, if the DEA accepts a picture, I would think Carnival would. I would call Carnival to make sure. Let us know what they say.
Also, I do not think you are legally supposed to have two copies of your driver's license or state i.d. so having a back up one isn't really an option. When I have gotten a new one before due to having lost one, the paperwork says that if you find your old one, you are supposed to destroy it.