Edge and Vibe don't require parental registration as long as the child is in the proper age group. Because kids in those clubs automatically have sign-out privileges, there's no need to create a password and provide a list of people with permission to pick up the kid.
If a tween who is not yet 14 gets CM permission to go to Vibe, a parent will need to sign a permission form, but that happens onboard. I am not sure if Edge requires parental permission for kids below the age threshold, but if so, that would also happen onboard.
If your daughter is 13 and going to Edge, though, you shouldn't need to do anything. She will need to check in with a cast member the first time she goes to Edge, and, as mentioned, the CM should have her name on a list of Edge-eligible passengers.