From one fluffy to another cruises are amazing for young teens. My DS's are 13 and 14 and are just about to go on their 5th cruise. We enjoy lots of other types of holidays as well. We went on the independence of the seas at Whitsun which is comparable with the adventurer of the seas. , and really enjoyed the ice skating and the ice show was amazing. Lots of entertainment is included. The only big expense is excursions and these are very much optional. I brought my boys travel band for the north sea to Norway but they didn't need them, actually I did not hear of anyone getting sick. I'd say it's definitely worth it but im quite adventerous with holidays and love my DC having new experiences. I buy my DS soda cards and they get unlimited drinks and charge up there sea passes for the arcades and that's all they need on ship. Your daughter doesn't need any actual cash but give money to the adults she is going with.
Definitely safe for your DC and she will love it! Cruises IMO are perfect for that age range. Not much extra costs at all- once you are on board, apart from drinks sometimes (buy soda cards) the food is all you can eat. I disagree with children missing school but it is one day and not your choice completely, if you know what i mean.
Go for it if you can afford it, it will be a great experience for her