If you bought the car and the car is in your name then it was you that should get the fine because it was unregistered.

Your daughter was only driving your car.  How was she to know that it was unregistered?  I don't think she has anything to worry about.  In WA new drivers have a limited number of demerit points before they lose their P plates.  For drivers in their first year they lose their licence with only 4 points and in the second year it is 8.  I don't know about other states.