First, congrats on taking the BIG step. My wife and I have been together for 32 years and it took us 27 before we took our first cruise.
As far as a passport, if you do the Caribbean all you need is a drivers lic and birth cert. BUT if your cruise tickets are in a different name like your wife's maiden name, you need a marriage license to verify her name was once something else. Iwas at the airport and witnessed this whole fiasco with a young newlwed couple. Believe me hassles are not what you want on your honeymoon. However, yes a passport is much better but remember your wife can't get the new one until she is married.