Scarier than a fire-breathing dragon: Character

So the writing's going. Not as well as I'd hoped, but going. Because I've been writing, I've also been thinking a great deal about writing. And along with that thinking comes the worrying. Oh, that word isn't right. Oh, horses aren't really purple, so don't write it. Oh, this is never going to be good enough, cool enough, hip enough...etc.

Certainly most of those voices should be whacked down with a hammer (at least for first-drafting purposes). But I do think that some of them deserve consideration, right from the start. Like this one: I'm afraid of writing a weak female character.

Some contextual notes: Yes, I'm a girl. And yes, one of my great dislikes of Twilight was Bella's character. And while I certainly don't think that it is the duty of the writer to moralize or preach to his/her audience, I do feel the need to present smart, strong, sympathetic female characters. And in this particular story, I'm a little afraid of failing.

Without getting too specific, I'll just say the following. My main character is a girl who falls in love with a human and consequently leaves her family and all she knows in order to be with him. Said human is a nice young lad (a prince), but not one who reciprocates the feelings (or even really knows she exists, when you get right down to it). So the girl pines away - but also gets caught up in palace intrigue and ends up playing a pretty important role in geopolitical affairs in this region. And she doesn't end up with the prince, but manages to get over that and learn about herself, etc. etc.

I was busy writing until I really thought about it and was instantly terrified that my main character is a horrible, horrible role model for girls.

My horrible response to this: But that's the way it has to be. You know, for character development! Arcs! She grows and changes and stuff!

My horrifically horrible response: And by the third book, she's totally kick-ass!

What do you think? Do writers have a responsibility to portray strong heroines? (I feel like I do, certainly...) And can my poor heroine be strong, even if she starts off the story in such time-tested weakling fashion? (I hope so...)