They are both correct, but only the first one is an independent statement. I don't understand your reason for thinking that 'Her father died when she was a small girl' is not correct, and I don't see why you think that one event occurred before the other. In fact, they were at the same time - the phrase 'when she was a small girl' is just a time phrase explaining WHEN the father died. He died during the period when she was a small girl, so the two uses of the past simple are correct. The second sentence is grammatically correct, but it is not an independent statement. You could only say it as part of a wider context, for example 'Jane wasn't able to go to high school. Her father had died when she small girl and her family couldn't afford the fees.' This is an example of one event (the father's death) occurring before another (Jane being unable to pay the high school fees), so the past perfect is appropriate.

2 is wrong. If he died before she became a small girl, you would say: "Her father had died by the time she become a little girl." 1 is probably what you meant.