I have been through exactly what you are going through. My daughter tested gifted at the end of second grade, and was almost a straight A student. She did most work on her own with no problem. She was a great reader in Kindergarten. After testing her for gifted, I enrolled her in a full-time gifted program at our local elementary school. Everything was accelerated a year. She was miserable. Cried everyday, was getting horrible grades. It was not what school is supposed to be...I ended up pulling her out and placing her in a regular third grade class. What a turn around. She is happy and is excited about school. Things are easier for her, and sometimes challenging, too. Bottom line is that even though a child tests at a gifted level, the program may not suit the child. And at such an early age, a child's impression of school should be a positive one. It's the later grades that your gifted child will excell and where it counts most.
There is little reason to be concerned at this point. She is doing what first graders have traditionally done. There is every reason to be suspect of a curriculum which attempts to teach skills which developmentally may be inappropriate. To some extent, if it were wise to be teaching children across the board how to read in kindergarten, educators would have done so long ago. This is not to say that there are not some children who are able to learn to read prior to first grade, but in general it is not a reasonable expectation. It may well be that your child is not a good match for this particular program, but that reality does not mean that there is something wrong with your child.