I am no expert on kittens v adults but the younger the cat is, the more active they will be. If they want out of the safe room that usually means they are not so afraid and you should try to give them the run of the house and see how they get on.
The main questions are what is in the room you confined them to and what times is she most active?
If she is bored she will manifest this by being very active and jumping around.
If it tends to be later at night this is extremely normal for kittens. The ‘midnight crazies’ reflect that fact that cats are naturally nocturnal and will tend to want to explore and play at night.
To be hones, if she wants to interact with you so soon after moving you should be delighted–a hyperactive cat has its own challenges but much easier to bond with than a scaredy cat. Try to give her plenty of climbing spaces, safe toys, and play with her a lot and I bet when she is 14 months old she will calm down and you will miss the old her.
BTW mine are two and they still run about at night. !!