Hi Gabriela,
Are there shops?!? Disney Cruise Line has some serious
shopping available and it always gets me in serious hot water with the hubby. These shops have a very large range of items and my favorite are the Disney Cruise Line exclusives. Each ship also has merchandise specific to them. You'll even find some adorable gift shops on Castaway Cay where you'll find some great beach items.
Okay, let me get back on topic. I can talk about shopping 24 hours a day! The answer is yes, you will be able to purchase diapers and toiletries onboard so don't worry if you forget something.
Also, here are a few tips. Your Daily Navigator is something to check out each day. It's the ship's daily schedule. Store hours will be listed and if there are any special deals offered that day, your Daily Navigator will have them. Please remember that the shops are closed while the ship is in port. I've found that the best time of day to shop with the least amount of crowds is in the evening after the second dinner seating.
Hope this helps and let me know if you have any other questions! Have a magical sailing!