How does the nanny feel about the arrangement? You say she's been through immigration at both spots; can she handle it solo with your daughter? If there is a clear advantage to this arrangement and all concerned are comfortable, then just have the documentation in order.

I wouldn't worry about my five year old going through immigration but I would be a bit more concerned about her nanny. Don't get me wrong; I love our nanny, but sometimes giving her instructions on going from Terminal A to B can be a challenge