I don’t think there’s any way to restrict access based on genre. Probably the best thing you can do is to add a Label to every movie you want to make available to your child, and restrict her access based on the label.
In case you don’t know, you can edit multiple movies at once to add Labels, so this isn’t as daunting as it sounds.
There are some existing feature requests for adding the ability to restrict by genre. You may want to add your vote by clicking ‘Like’ on the first message in one of these threads:
(Recommended: has the most votes, better feature description)
Others (forum admins should consider closing these and redirecting to the one above:
