You usually can't apply quaternions directly and it's usually a bad idea to try and do so.
If you want to modify the object's rotation directly best suggestion I have is to modify the eulerAngles. It's much easier to use as it's just a Vector3.
For example something like:
transform.eulerAngles = Quaternion.LookRotation(newRot).eulerAngles;
I haven't tested the above code but I've got something similar running in my game.
Hope this helps