not to worry. Any cruise is what you make of it. You said yourself " the dates are perfect, ports exciting, ship is top-notch" you have the totally right attitude to sail, go for it.
Celebity is not a snooty, snobby cruise line, your fellow cruisers who choose Celebrity appreciate the fine cruise ship experience that is Celebrity. You will find folks of all ages aboard.
Will there be tons of kids running around on board? Probably not.
Most of your days at sea will be spent by the pool, i don't know of many kids who don't like to spend all the day in the pool do you??
I would bring some small toys, books, coloring books & crayons for your daughter to play with.