very adorable little girl!
the photos taken with the easy share are all out of focus and seem to have quite a bit of noise. I'm not familiar with the 'easy share' cameras, other than knowing they are usually point and shoot.. so those type of things may not be so easily corrected?
the last photo is a lot more crisp.
wonderful candid photos; definitely ones for the scrapbook
My impression is that for most you moved closer to your daughter, i.e. your subject, than the lens of your camera allows. The last, which was taken outdoors, in good light, and is not quite as close-up as the others, worked a lot better.
Often the lenses of compact cameras do not allow you to get any closer to your subject but 70cm (roughly, and sorry, I don't know how much that is in inches), unless there is a little "macro"-setting (which on my compact is marked by a flower-icon) ... pushing that would allow you to get closer, and by putting in the "macro-setting", the lens opens up wide and gives you a shallow DOF (depth of field) for a nicely blurred background behind whatever it is you want focused in your photo.
Having determined that the one photo of your daughter outdoors in good light (and not too close up) is the sharpest of all, I would suggest you really try to limit your shooting nice portraits of her to the outdoors. If the in-built flash is all the additional light you have (to up ambient light, which will be far too little for the lens your camera has), then better refrain from taking photos indoors. That direct flash makes faces look very flat, often gives you red eyes (see Photo 3), and produces ugly shadows right behind your subject.
So it seems like - with a beautiful model like your daughter - you fare best outside in good light. Need not be bright sunlight, to the contrary, an overcast sky takes away strong shadows as the clouds are your "big diffuser". Too little light or indoor photos do NOT work as well...
And watch out for the minimum distance you may take up to take photos of a person. Better crop later than produce a blurred face and sharp background, as happened in the last but one pic shown here.