I remember well those overwhelming early days when my DD was diagnosed (5 yrs next week). You will -- all of you -- get through this. The good news is that you now know what was making your daughter ill & her insulin will let her function again.
The website
www.childrenwithdiabetes.com is very helpful.
We are going on our 1st cruise in December so we are not seasoned
DCL passengers. Our 16 yr old DD & her 3 younger sibs will be with us too. I do know that you can have doc sign a Medical Circumstances form (from TA/DCL) and get a real fridge in room for her insulin.
You need to learn to carb count -- even pack a guide with you as trip is pretty soon. Measure & weigh some food at home so you get an idea what a cup, 1/2 cup of cereal, pudding, etc. looks like. Ounces of cheese, meat, etc. This will help you keep on track with her diet plan. Start reading some labels on bread, bagels, ice cream, etc. (some of these vary wildly) for carbohydrates & fibre. I would think you'd want to make a Family rule that Meal time will be Family time rather than letting her go to meals with the Club. This way you can steer her towards better choices for her diet & count her carbs & increase her insulin to cover any special treat desserts. Have the whole family together at this time to share your day's activities so that your DD w/ diabetes is not singled out having to leave the Club.
She should understand firmly that she is not to have ANY regular pop/regular Jell-o or more than the 1/2 cup juice you see her have at breakfast with you. She can have Diet Pop/Diet Jell-o & water's best for thirst anyway. Be sure the CMs & waiters know she has diabetes so they don't inadvertently give her some of that or make a big deal of handing her a giant sundae thinking bigger is better -- not in this case! I would be cautious with any smoothies/milkshakes. They can contain as much as her whole day's worth of carbohydrates in that 1 drink. Small amounts, share things, take smaller slices, pieces, etc. of decadent things if she really wants to try something, especially if other kids are having.
She doesn't have to have only diabetic-choc/sugar-reduced goodies. Though I'm sure you can easily request these on DCL as the restaurants are very accommodating at WDW. These sweeteners can often give diarrhea. Moderation is the key. But there will be so many different goodies on the Cruise that she doesn't need to feel left out. She can be active also to counter some of the possible over-eating. Room service nightly in your room will limit the temptations at bed-time snack time & make cheese, crackers, grapes & a chocolate chip cookie awful special for all to share.
Also be sure the CMs & the kids you are travelling with know the symptoms of a "hypo" (low blood sugar) & how to so easily treat it. Give her 1/2 cup NORMAL pop/juice & don't leave her alone. Then page/get you. Even though it sounds like food is everywhere on the boat I would be sure to carry & have her carry on her a sugar source just-in-case (individual sugar cubes/life savers if you think she won't just eat them as candy). Do make sure you have quick-acting sugar source & a snack on you if you are going off boat on Nassau day. Do get her a Medic-Alert bracelet too!
We always travel with extra insulin packed separately in case anything happens to the 1 set. Also take an extra glucometer & battery. We also have a note from doc that DD has diabetes & therefore needs the syringes in case of any questions at border-crossings.
Getting up at regular times & eating at regular times is important. Sounds like that's doable on the ship with all the activities & the fact that your dinner is regularly scheduled. Do request early dinner -- normal dinner-time. Let your Dietician & Educator Nurse know and they can help you with the planning.
The DisAbilities board on here also has several helpful people with Diabetes knowledge.
Long post, sorry. I truly feel for you, your DD, & family.

You will all have a fantastic cruise still though!