I'm in a similar situation with my DD10 and DS6. While my DD is gifted, my DS is way out there and quickly catching up with big sister academically. There are times when she handles it well, and it is great to hear them discussing books together that they have both read or exploring a science question. However, she can also be very competitive with him, and I can tell that it bothers her that he knows the things he does/is able to do the things he can. She will try to put him down and in his place because I suspect to make herself feel better.
She knows that he is advanced for a first grader, and she seems to be okay with that. I think she just doesn't like to be challenged by her younger brother. How do I help her feel confident about herself? She is a wonderful, gifted girl herself, but I see her self-esteem taking a hit and her doubting her abilities.