Young Rex hates her cage

Question
Hi, my brother just got me a four month old female silver seal Rex Rabbit. I've had her about a week now and she cannot sleep in her cage while the door is closed. She's a house rabbit, doesn't mind going in her cage in the day while it's open but in the night when I go to bed I close the cage door (for her safety) and she cannot seem to sleep there. As soon as the door is closed she tosses the bedding out of her cage, scratches the floor to it, knocks over her food dish, bites the bars of the cage and paces several times throughout the night. I've tried inciting her to stay calm by placing food and timothy hay all over the cage and even a bit of fruit but nothing works. Is there anything I can do to make her more comfortable and less jumpy during the night?  I'd close my door and let her roam but it's summer and the fan stays on in my room as well as she loves to nibble my books when I'm not in room.

Answer
hi-sorry so long answering.
you will have a big problem with her as she will nibble cables etc if left out -maybe another bigger cage is the answer but then again why not put the cage outside in the garage or shed. this way you will have no problems listening toher in the night.
dave.