We've done 2 Disney cruises ( a 4 and a 7 day). Dining on Disney is unique because both ships have 3 restaurants (in addition to the adult's only venu which is well worth eating lightly at dinner with the kids and schedualing a late night reservation for). The way it works is: you will, along with your waiter and wine steward, rotate each night to a different restaurant. One night will be at Animator's Palate (on a 7 day it is the most popular site for passengers to request triplicate dining nites), another will be at Parrot Cay, and the 3rd at either Lumier's or Tritions (depending on the ship). The night you are schedualed for Lumier's or Trition's (for the 3 day cruise) will determine your "formal night". We enjoyed that each night we knew that a portion of the guests would be dressed up-it also made for easier reservations in the hair salon (with only a portion of the ladies dressing up each night there was far less demand for those who wanted appointments).
As far as the dress went-it ran the gamut-there were those (us included) who prearranged tux rentals (it's great, they are waiting in your stateroom closet when you arrive) and dressed up fancy to have family photos taken, there were men in sports jackets (and tie) and women in nice pant suits-you would not feel out of place if you didnt want to "dress to the 9's". My daughter (then 8) wore a nice church dress, and our son (then 6) wore dress pants with a little collared shirt and a vest. The rest of the nights a man/boy would be comfortable in dockers and a polo type shirt-women/girls would be comfortable in even a skort and blouse.
As far as packing goes-take what you will be comfortable in-the dress is very informal-unless you want to go to the nicer lounge with the pianist or go to Palo's (the adults restaurant). You might want to throw in a tropical shirt or dress-they always have a tropical themed deck party one night, we have also found that you get smiles with unique disney character shirts (we sailed soon after the 9-11 events wearing Mickey saluting the American Flag-we were deluged with requests on where they could be purchased). Disney does'nt provide robes-so you may want to bring a lite cover-up, and the ship's stores are VERY LIMITED in their clothing items (not much beyond t-shirts and socks) so don't count on being able to purchase a clothing necessity on board.
You will have a fabulous time! The crew is genuinly nice and the staterooms can't be beat as far as space, storage and "Disney magic" (think "Minney's House" in Toon Town as far as some of the whimsical touches go). The kid's programs are such that our 2 have to be pulled away from them to join us for family time. There's also plenty of adult things to do.
Enjoy your trip-if you would like an advance peak at a sample day's itinerary let me know-I can scan it and send it e-mail.