In general, manga and anime do this character type better than Hollywood. With Hollywood, the "I'm too independent for you" aspect begins to wear thin. Even Eilonwy, Taran's love interest, grates some. She is funny with a few great lines. But she always seems to be right, even when she truly shouldn't be (gatecrashing a military action), and she is regularly dismissive of Taran, even if she does it defensively. (I don't remember my reaction to the character when I was younger; I was more enthralled by Taran and by Gwydion than by Eilonwy. I do remember that I liked her in the third book the best.)
In comparison, manga and anime present this same character as hapless AND effective at the same time. Check out Kasahara from Library Wars, who is somewhat spastic and committed to her career and brave and rather innocent. 
And then there's Sophie in Howl's Moving Castle: tough and whimsical and unsure and efficient and passionate. Wry and adorable and real all at the same time. (And it occurs to me that Miyazaki would have done a beautiful job with Alexander's series. Perhaps his studio still could.)
Anne of Green Gables, of course, is the Western answer--in both the books and Sullivan's first series. And Anne is wonderful. But she is difficult to replicate. Off the top of my head, one exception I thought of is Amanda Bynes in the Shakespeare-inspired She's the Man. She is a decent comedian and willing to do physical comedy where she falls over her own feet.
Another exception, surprisingly enough, is Ziva of NCIS who has a somewhat similar--if much more inherently violent--personality to the anime/manga female characters. She also has a notable internal arc).
That sense of whimsy makes all the difference. And a great actress. And having a storyteller--Bellisario--at the initial helm.
