Last year on our cruise I carried a 12 pack of Diet Pepsi (my beverage of choice) and a 12 pack of bottled water on the ship with us when we boarded. No one said anything to our family of 4.
If you check the Carnival site you will find that you can bring a reasonable amount of beverage on board.
Have never done the alcohol thing as we are not big drinkers and find the adult beverages to be fairly priced.
Either way, enjoy and have save travels.