Chex Quest. It was originally a cereal-themed overhaul of Doom that came with specially marked Chex cereal boxes. Apparently it was popular enough that the makers released a Chex Quest 2 and eventually a Chex Quest 3 and made them free to download.

It's pretty primitive by today's standards, but still a blast.

Well...thanks for posting...

Uncharted or Uncharted 2. If you have PS3, that is. If she doesn't like story (which I probably guarantee she will) there's a great multiplayer. I's a T rated game, you can only see blood in the cinema mode, and there's little profanity (like damn and hell) so it's a good ol' clean game. Portal 2 is a weird game. It has some jokes only advlts would be able to understand, and some crude humour as well. And it's not all that clean profanity wise, as Wheatley calls the detective turrets "crap turrets." So take these things into consideration and see if the game is right for her.

Also, Republic Commando.

This forum Rocks! I really thank you all for posting your suggestions!

Yes, yes I do rock don't I?

I'm sure you can find a bazillion old Doom or Quake mods nowadays to fit your style. I was maybe a couple years older than your kid, if that, when I first played the former, unmodded.

Don't forget about the Flood. It would probably scare the hell out of his niece, and not to mention the fact that you can blow them into as many pieces as you please.
Halo Reach maybe, it doesn't have the flood in it, but I haven't played it in so long that I couldn't tell you the level of profanity in it.

Timesplitters! Quirky humor and funny multiplayer characters. I don't think there's much blood.