Call me crazy, but I'm thinking of Barbara Gordon being played by Dakota Fanning. Before you go nuts....
-She's fourteen now, which gives her roughly until age sixteen before they start shooting with her on the third movie (i think #3, if ever, is the best place to introduce a sidekick)
-She's been acting longer than most 14 year olds, and she's pretty good from what i've seen. she could handle working with tom cruise, so i think she'll be okay with nolan/bale. unlike many of the other suggestions on this post, this girl can act.
-Finally, just look at her face!
Compare that wide grin to batgirl's...
Now I know what a lot of you are thinking. "She's way too young to play barbara gordon, are you ******ed?"
My answer is this: Jim Gordon is already a well established character in this incarnation (gary oldman rocks!), and introducing his daughter would be a perfect lead-in for the batgirl character. But the twenty-something sidekick thing has been butchered under joel shumacher's ridiculous vision. so i suggest the notion of making her much younger - dick grayson young - and I'd make her serve the same purpose that robin would in terms of developing bruce's character.
as someone posted earlier, a teenager fighting crime doesn't make a lot of sense. this is true. however, a teenager with a police lieutenant for a father and gotham city for a playground is bound to turn out pretty badass. not to mention batman will supply her with all the batarangs she needs....
I doubt nolan will see it this way, but I think it would be a cool way to do the batgirl character. I'll probably write a fanfic based on this just to satisfy my own imagination