Dear Triptakers:
I am the new family cruise editor for CruiseMates.com. My seven year old's first cruise was with Celebrity aboard the Zenith to Bermuda. She was just three when we cruised and she loved it! (She's since been on 8 other cruises and has enjoyed them all.)
Kids are welcome to come to formal night and generally the older set loves to oooh and aahh over how cute the little ones look dressed up. (Obviously kids' wear is less formal than adult wear...) Or, alternatively, you could get a private babysitter for the formal nights. If you wish to get a babysitter, note that formal nights are popular so go to the purser's desk the first day to make your reservation for a babysitter. We used a babysitter one night on our Celebrity cruise and the woman was capable and very sweet.
Most cruise lines do allow toddlers to use their youth facilities if accompanied by their parent. It's a good way to get access to crayons, games, etc for your child. Talk to the counselors at the beginning of the cruise and see if there are any problems with this. Also, often there are better times of the day for you to bring your daughter, when the youth room might be less crowded. (First thing in the morning is usually a slower, quieter time in the youth room.)
Lastly, my daughter just loved how the Celebrity waiters doted on her. Dinner time was certainly a highlight for her because of all the attention she got! I'm sure you'll have a great cruise!
Luisa Frey Gaynor