Gimp can be frustrating, but it's one of the most amazing and powerful free applications out there. You're right...what you're trying to do is very simple, but you need to know a few tricks to get it to work well.
First, you need to use .PNG as .JPG files don't support transparency. When you try to save a file in .JPG that has a transparency, or alpha, channel, you should be prompted to "export" the image by flattening all layers, which essentially replaces all the transparent areas with the current background color (usually white).
Second, there's a tool that's been added to the most recent versions of the Gimp that does exactly what you want to do. It's called the "Foreground Select Tool" and is really simple to use once you get the hang of it. This tool was added in Gimp 2.4, so you'll need at least that version or higher to use it. This tool uses a two-step process: first you draw a rough circle around the object you want to cut out (your daughter), then you "paint" over the foreground object so the tool can sample all the colors you're wanting to extract. This sounds strange until you do it...once you understand, it's really pretty simple. You can read the docs for this tool here
. There's also a YouTube video
that shows the basic process. Apparently no sound on that video, but at least you can see what to do.
Not sure what was happening when you tried to use the scissors. There are so many variables, it's hard to tell. You probably didn't need the extra step of adding a transparent layer...when you had your selection copied to the clipboard, you could have used "paste into" or "paste as new layer" or "paste as new image" to get what you want.
Let me know if this doesn't answser your question.
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