Here's another: you're searching on any keyup which creates lots of overhead. Google's implementation is more complex. It appears they search immediately as you type the first few characters on each keyup/down then if the word goes over a few characters it switches to querying every couple seconds, or until you hit the spacebar. It also seems like they have another timer if you pause after a second or two.

If it's just you using this, I would say don't give a crap. But if you plan to allow others to use it and it gains a userbase at all you might consider a similar approach for obvious reasons.

Cheers!