My rabbit wont let me pick her up?

Rabbits hate to be picked up so this is normal but it is terrible that she has not had any exercise for one month. You need to just pick her up even if she does not want you to so she can have some floor time. You could try to put a box or something there and guide her in it so you can pick her up in that. As she is new you should get her checked out at the vets just to make sure everything is ok. If she does not have enough exercise her spine will end up deformed due to being stuck in a cage.