A formal assessment of her strengths and needs is important. Discuss this with her current teachers and see what they think about her social and emotional adjustment to working with a group of children who are a year older.
Meet with the school folks and discuss your concerns. What are your options? What teachers could she have and do they have any special knowledge and skill in working with gifted children? Have other children "skipped" kindergarten at this school? How did they do? Will her first-grade teacher work with her to provide the support she'll need? Moving into real school can be a big adjustment, and her classmates will have had a whole year to get used to this. First grade is also a very big learning year and both combined -- even for a gifted child -- may feel overwhelming. Ask about other options as well. If she stays in kindergarten, what would be done to enrich her experience? Would she be able to go to the first-grade room for reading?
Talk with people who know your daughter and whose judgement you trust. Listen to them, but ultimately you will have to follow your heart and head and make the decision you feel is best.