Two questions for you.
Will the gun/ammunition be stored in her room such that she has no access to it. (No key, doesn't have the combination to the lock. Cannot, in any way, get into the storage conainer,)
Does she have a FOID card? I am assuming that you have a FOID card.
If she doesn't have a FOID card she should get one and she will be OK with access to the gun/ammo. IF she doesn't have a FOID and, for whatever reason, the police show up and find the firearm/ammo and you are not home she may be going to get a free ride to the police station if the gun/ammo is in her room and she has access. That would end up being sorted out in court.
If she has a FOID card she can have access to any legal firearm and ammunition, otherwise, keep it in your room locked up, with you having the only key/combination. I recommend that she gets the FOID. That way you can also take her to the range and legally teach her to shoot.