Hi sprklbry, and welcome to cruise-chat.com!
As a parent, I understand your concerns. Our son is now 14, but we've been cruising with him since he was a baby. Carnival does, in fact, have a strict sign-out policy when it comes to kids your daughter's age.
My suggestion is for you and your family to go to the Camp Carnival orientation they will have the first night of the cruise. This is usually held in one of the smaller lounges. The counselors will tell you about the programs and explain their safety procedures.
I'll also add that it's not mandatory that your daughter use the program. We have many fond memories of our son hanging out with us when he was younger. (Actually, he still does.) Yet, it is nice knowing that the program is there, so I do suggest signing her up that first night. She doesn't necessarily have to go for hours every night... our son was usually satisfied with a couple of hours after dinner depending upon the activities offered.