Some cruise lines do not allow you to bring your own liquor onboard. Disney is not one of these. No problem with bringing it in your carry-on luggage.
If you buy liquor at the onboard duty-free shop, you will not receive it until the night before your disembarkation.
If you buy at the islands, you may drink it onboard, however you are not allowed to bring an opened container back into the United States at the end of your cruise.