Here's the thing with self defense, you're allowed to use "justifiable force." What this is largely depends on the situation. Yes, the kid was throwing bricks, possibly endangering the life of the woman. However, the kid was twelve.
Honestly, if I were that kid's parents, I wouldn't press charges simply because he was being a complete moron and harrassing the poor old lady. Like most people who do that, I'm sure the kid had had, at some point in time, friends to help him harrass her.
Honestly, she probably pulled the gun and told him to stop, he acted like he was going to throw a brick, so she shot him. Believe me, if he was close enough to be throwing bricks into the house, the lady probably had a good chance of hitting where she was aiming. I mean, he is twelve, how far can he throw a brick? Besides, it was on her property, she had every right to defend herself if she felt she was in danger. I've had stuff thrown at me before, and I'll tell you, bricks whizzing by your head makes you a little concerned for your life. Legally speaking, she might have even been justified in killing him.
If she does get charged with something and I was on that jury, I'd give a verdict of not guilty. Sure, she could have handled it better, but how calm can you really be if bricks are smashing through your windows?