I think your daughter will have a ball, just take her to the kids area the first night and I bet she finds friends there for the entire week, kids actually love going there. I wouldn't worry that she will not enjoy herself, you too for that matter. Rhapsody is a lovely ship, enjoy!
Rhapsody is a beautiful ship - you're daughter will love it (our grandkids were with us last June, ages 7 and 12 and they had a wonderful time). My kids never do the kids adventure program they would rather be with the kids down by the pool. If your daughter decides she doesn't want to do the program you can pay $5.00 at night and they can go up there with the other kids. Sometimes my 12 year old grandson would do this with a friend he met. He didn't want to do the program during the day (would rather do his own thing with new friends), but at night they might have a certain program planned that he and his friend would want to do. The $5.00 is paid in cash, it is not put on your sign card. Hope you have a nice trip.
We were on the Rhapsody last April. My then four year old was a little too shy to do the planned activities, unless there was someone in the playroom he knew. So it really depends on your child's personality. The children are divided into four age groups and there are planned activities throughout the day and evening. I wouldn't worry about your daughter having fun, but I do recommend she bring along some of her favorite toys, activities or games. The library offers limited numbers of board games and children's books you can check out and return at the end of the trip.