What's a good, FAST point and shoot camera?

I just came into a small windfall of unexpected cash. While I’m saving most of it, I decided that I need a new camera as my last one broke and the free replacement a relative donated to me is not working out very well. I’m having trouble figuring out which point and shoot I want to buy. I have read several different review sites and am more confused than when I started.

* Price isn’t much of an issue, but I don’t want it to be too expensive in case I lose it (I lose lots of things, so that IS an issue) I probably would like to spend under 350$

* I want it to be fairly sturdy. The last one broke because my daughter got a hold of it, managed to open up the lens and then dropped it. She’s getting older and more careful, but I don’t want anything with little fiddly bits that could break off too easily.

* FAST FAST FAST—trying to snap pictures of a toddler is rough. She rarely looks anywhere near the camera for more than a second and many shots I take start out looking great in the viewfinder, but by the time I snap the pic, she’s already moved her hand in front of her head and turned around in the opposite direction. I HATE pressing the button and waiting a second or two for the click.

* decent quality shots in low lighting—So many indoor shots ruined because of low lighting problems – I’d like to have better luck with that.

* Pocket sized—I don’t want something that’s too bulky because then I won’t carry it around—or if I do carry it around I will be likely to lose it. Small is good.