Your daughter cannot be out with her own firearm with a Hunter Apprentice card. You must share 1 firearm with her, and she must be within arms reach of the licenced hunter (most likely you) at all times, when she has the firearm. Any game she takes while out with you comes off your licence, with the exception of migratory birds; the Feds require she actually have her own waterfowl licence for some reason.
And, she must have completed and passed both the firearms safety course and the hunter Ed. Course.
When she is 15, she can obtain her full hunting licence. At that time, if she has obtained her Minor's Permit for firearms, she will then be able to legally borrow a non-restricted firearm to hunt with and do so without your immediate supervision. Without that permit, she cannot borrow a firearm.
ETA: Forgot to mention that to obtain the firearms minor's permit, you will need to call CFC directly to request the application as they do not make it available otherwise...and again, she has to have taken the firearms course first, and passed both exams.
This is the exact route I took with my nephew.