Hi bendwilliams, and welcome to cruise-chat.com.
No, you are not crazy for taking your daughter, but be prepared to spend a lot of time with her. I speak from experience, as our son had already been on four cruises with us by the time he turned three.
You're correct in that she won't be able to use the pools. This is actually a policy of the U.S. Public Health Department.
Yet Celebrity offers what it calls Toddler Time, where you can accompany your daughter to the Kids Program. Information will be in the separate Kids Club (or Fun Factory) daily program. If you do not receive one automatically, you can find these in the Kids' Room up on "The Lawn Club" Deck.
Happy to answer any further questions based on our experience.