Personally, if I were writing a girl!Harry fic, I would significantly alter her relationship with the Dursleys, and through that her views on the magical world. Let's call this theoretical character Daisy, in order to distinguish her from other female versions of Harry.
Petunia does see more of Lily in Daisy than she does in Harry; however, instead of outright rejecting her, she sees Daisy as a version of Lily that can still be saved. So on one hand, she would be more "loving" towards Daisy, but on the other, Daisy would still be harshly punished for any accidental magic. For Daisy, the punishments would be more traumatic; unlike Harry, she wants to please the Dursleys, and it's the rejection that really hurts. Instead of being thrilled by the magical world, she hates it - she wishes she was normal, so her family would love her. At the same time, she's desperate to please those around her, and the magical world is all she's got.
Overall, she'd be less of a rebel than Harry. I doubt she'd make Gryffindor, though if you wanted to keep the same cast you could make an argument for it. Nor, however, would she be in Slytherin, like in other AU fics; Slytherin is overly proud of its magical lineage, and Daisy would loathe that aspect of them. Instead, I think she'd fit better in Hufflepuff. At first, she just wants to be accepted by anyone and will do anything to fit in, but eventually she learns the meaning of true acceptance and loyalty.
The main issue with such a character, story-wise, is that I think Daisy would basically start out as a less intelligent version of Hermione, almost painfully afraid of breaking the rules. And unlike Hermione, who gets kind of dragged into things by Harry and Ron at first, she'd have no motivation to get involved in the plot. Plus, I think GoF and OotP would leave her traumatized and depressed - not exactly a character arc I'd enjoy writing.
Note that, I don't think this is necessarily specific to a female Harry; a similar AU could be done with a male version. In fact, this goes so significantly beyond making him a girl that gender would be incidental to the plotline. However, as far as using a genderbend to take dramatic liberties with characterization goes, I think this is more reasonable than a naked ninja-druid sociopath.