We sailed Majesty in Sept. but we don't have kids. Most of the ones I saw looked happy; the conversations I overheard were generally positive.
My 1 caution: I never saw a life guard at the pools. Make sure you're watching your daughter & that she's a good swimmer. The pools aren't long but they are deep.
Coco Cay is great for kids; felt like a big kid myself there. Keep her with you but the open air straw market in Nassau can be fun for kids. Let her haggle & get something she wants. My friend's 13 year old had a blast there.