Imagine what happens when someone falls or jumps down from a height. The hair stands and falls down with a delay as you land. Running like your character does creates a less extreme effect like that. You've recreated it fairly well on the back, but the front bangs should perhaps behave a bit like flapping wings. The top of the hair on the other hand probably shouldn't bounce like it does now at all.
In one frame the outline is two pixels wide on the back, it stands out too much and creates a blinking effect. As for the anti-aliasing on the top of the head, it should look better if you reduce the double pixel ones to just one as well.
