I'm selling a car to my daughter but I'm not going to lower the price.
Why wouldn't you? Is there a reason behind that?
She should have to work for it.
It is good to want to hold firm on a price. You can be teaching her a good lesson to be independent and not expect someone else to rescue her.
I just wanted to make her earn it so she learns the value of it.
Well even though she is family, it doesn't mean that you should make it easier on her. It would make it so that she doesn't understand the value of money so trying to get the best deal for your car is a smart idea for her to learn more about finances.