Thanks, everyone!

You have a very good grasp of the technical errors in this image, some of which could have been combated, as others mentioned, by swapping seats with your friend. If you had this same scenario with a DSLR, you could have remained in place with wiggly toddler on your lap and simply expose for her face and not the light streaming in the window. The point and shoot merely saw the vast quantity of light and exposed based upon that input.

I used CS3 to rework your image. I first opened it in Camera Raw, which allows a lot of easy corrections before even entering PS. I bumped exposure to +2.1, added fill light, inc. the brightness by +5 and added contrast to +13. I also went into Hue/Saturation and adjusted the reds and oranges for her face. Finally, I brought the noise down by adjusting Luminance to 39. Now I open into PS.

I cropped to minimize the clutter, but I didn't remove it completely. I am not good at extracting like AJ, so I don't even try! I then went to Filter>Sharpen>Unsharp mask to sharpen some details. I then did Filter>Noise>Reduce Noise to remove some of the graininess. Finally I went to Layer>New Adjustment Layer>Exposure and moved offset to -0.0294 to add a bit more contrast to the image.

You can see my finished product here:
http://www.flickr.com/photos/31335390@N02/3974127603/

I'm not sure about correcting the exposure, as I know nothing about PhotoShop. I think it might be possible, but I'm not sure how.

b/w edit:
http://i7.photobucket.com/albums/y286/NanasMama/DSCN4804editfinalbw.jpg

You have a really good grasp of what went wrong with this shot. The backlighting confused your meter and resulted in a really underexposed subject. I extracted her from the background and lightened her repeatedly using curves. I ran noiseware on full strength and layered some textures behind her (not at full opacity). Then I added the sunflare. I'm not sure you'd want to do this to every picture that turned out this way.
Next time you'll be brave! and bold! And ask her to switch places with you so the light will be on her face and not behind her. There's nothing wrong with a point and shoot or a camera phone. You can get great shots if you keep an eye on what the light is doing and know the limitations of your camera inside and out. And actually, I really like those big windows at fast food restaurants for good catchlights .
Good luck in your photographic journey!

Maybe some vignette? Or a "glow" kind of effect? I'm thinking of the "glow" tool in Picasa, but I'm sure Photoshop has something similar.

Good luck!

You are right, she is a beautiful subject.

I probably would not have taken the photo shooting directly at the window, and with all the "stuff" on the table. I probably would have posed her standing next to the window, so that the light coming in would have illuminated her but not drown her out. When shooting into a lit window it sometimes makes a silhoutte of your subject. Which is cool if you intended that look.

I would play with Camera Raw in Photoshop with the Exposure and Recovery sliders. I'd also tone down the brightness and increase the fill light slightly.

Then I may do a black and white conversion to balance out some of the graininess.