At first glance, the main problem does look like noise, but there's not an easy way, as far as I can recall, to change the ISO on these cameras... I do know, though, that the EasyShare PC software had this filter that can be applied that makes it look like it was painted using brush strokes which is what it looks like particularly in the areas around her collar.
So high ISO-related noise for sure, but check the settings on your computer to see if this filter is turned on by default. It's been a while since I used the EasyShare software so that's as much information as I can provide.