I had an excellent father. He wasn't perfect, but his imperfections and occasional impatience made him more human and relatable. Don't pretend to be perfect - let her know that everyone makes mistakes not just by saying it, but by showing them yours. Our world has become better for women to live in, but there still is a silent pressure on women to be flawless. Physically, emotionally, academically, professionally - we are not supposed to show weakness if we are to be taken seriously. Show her it's ok to be imperfect, this will be even more meaningful coming from a male role model.
And I'll echo what others have said - listen to her. Even if it's stupid ramblings about her favorite band or what a classmate did or any number of things you really do not care about. When she feels heard on the little things she will know she has a voice in the big things.
Lastly, be honest with her about the world not being fair. This was something my dad maybe could have done better. I was supported and told I can do anything a man can do, but I wish I would have known a little sooner what societal obstacles I was actually going to face. You don't have to make it sound ok or even acceptable, but all girls should know what they're up against so they can be prepared to face it head on.
Was his first name Xavier? Dr. X Wiener?