I wrote to you last night but it took so long that my efforts disappeared into the web! 
I don't know how old your daughter is, or any details of her temperament, so take the following comments in that context. What I am going to say is pretty universal, however age will have an impact on a young person's learning profile. I say this having at one time been a teacher for quite a few years, in some cases teaching blind and autistic people to use computers.
Photography is a wonderful mixture of art and science, which is probably why it attracts so many technical types who have an artistic streak! 
Becoming a good photographer needs one to learn the elements of artistic design - how images should look to be pleasing to the eye if you will, and that can be achieved by studying the works of successful artists: painters and photographers. The basics can be achieved by going to classes, reading some of the many great books on photography or going to sites such as Lynda.com.
The second element is to understand how light behaves and how to manipulate the controls of the camera that help us manage those characteristics. There are options here with most modern cameras: initially one could stick to the automatic or program settings and concentrate on getting the elements of image layout right. Eventually however, one should move to at least the semi-automatic controls such as Av (Aperture Priority) and Sv (Shutter speed Priority), in some cases one may move to fully manual mode to make images that the built-in algorithsm cannot manage.
The issue, from what I understand, is that your daughter has not learned the controls of the camera and perhaps the understanding of how light works. It may be that she has a sense of what a good image layout may be but can't control the equipment to get what she wants - which would be very frustrating for her. This will not be solved simply by getting a new camera, but if you do decide to get her one, as an incentive you could make it conditional on her learning how to use the controls: she could do that with her existing unit as the controls should be very similar.
I understand that she has a fairly high degree of anxiety and that can be a big block to the learning process. Stress shuts down the neocrotex, the higher learning functions of the brain, and we revert to the lymbic part of the brain - basically the fight, flight or freeze reaction. To reduce this possibility it is important that she has a structure within which to learn, and that the learning style matches her personal pedagogical profile. It is important that she sees a learning path that can be achieved in manageable steps, so as not to overwhelm her. Without doubt her age, maturity and emotional state will have a significant impact on her learning potential.
People have different learning styles: some learn by reading books, some watch videos, and some prefer the interactive experience of the classroom or the coach. These days children’s brains are generally wired more to short, discrete learning experiences that may be best delivered through the web, with which they are usually very comfortable. If that is the case with your daughter I would recommend using web-based tutorials – there is a host of them available through Youtube.com, (some are better than others), but as I suggested previously I would recommend seeking to see if you have free access through your library to the lynda.com website. It has excellent training paths from absolute beginner to advanced topics. The lessons are structured into a learning path, they last usually a few minutes each and in some cases have sample files one can download to practice on (for learning image post production if that is a consideration). After completing each course, related topics are offered for further education.
If she is comfortable with doing so, it might be a worthwhile thing to consider for you to learn alongside her – you seemed to get a kick from taking that photo last night! You will be familiar with what she is doing and you can help her if she gets stuck on a subject. In that case if you each have a camera you can work side-by-side - perhaps you on the existing camera, and her on the SX60HS.
