It is a tough decision.. everyone knows their own children the best. Some children are more self reliant than others.
On the 7 day, boys were very comfortable with being on the ship alone, loved being with the other kids in the LAB, and this was their 2nd cruise so they had a comfort level and they weren't alone, each had a brother with them. I think all that helped too.
On our next cruise, both want sign in and out privileges, DS 12 , soon to be 13, wants to be a teen cruiser and just have the run of the boat... not sure how I feel about that but...that's a 2004 worry.