HI: On US cruises you must be 21, the easiest way to avoid it is to have a beverage in your room (thats is you are old enough) then you can drink in there and not have to worry. In addition depending on how old she looks I have never known a bartender to card anyone. Usually you don't carry anything with you except your room card; you could do the ordering and then there is no question.
Good luck, I think whatever cruise you choose you'll be happy. A good first time cruise for young people is Carnival!