Hi Cinbride! I see you're from PA - whereabouts? I'm from the Pittsburgh area.
I have the SX10 IS; I upgraded from the S3 about a year ago. I've been on the fence for a LONG time about making the jump to a dSLR. But I know I'd get infected with GAS (gear acquisition syndrome), and come fall we'll have 2 in college at the same time, so a dSLR just isn't in the budget right now.
Anyway, you asked about the "i" in your viewfinder. That's a good thing! The IS in the camera name stands for Image Stabilization, and the "i" in your viewfinder means it's turned on. It's supposed to help you get sharper photos when you're shooting at shutter speeds where you might get a little shaky.
As for that adorable photo of your daughter, I didn't see anything wrong with it. Yes, fill-flash will get rid of some of the shadows, but I don't think the shadows are that bad. (But that's just my opinion) If you try fill-flash and it's over-exposed, you can adjust the amount of flash - press the "func.set" button on the back and in the menu that comes up, about half-way down is the flash adjustment.
It's a good camera, and once you get the hang of it and learn all the things you can adjust, I think you'll like it. The main area where it's lacking is low-light photography.
Any other questions, just ask away!