Welcome, GCN3030!

A few things which may be of interest -
1) post: roundup of early gifted traits
. . (yes, your child appears gifted)
2) book: A Parent's Guide to Gifted Children, by James A Webb PhD, et al.
. . (cautionary tales about the road ahead)
3) thread: advocacy
. . (prep for finding a good "fit" in schools/programs) Three cheers for homeschooling

It is important to ensure that learning is student-led, following the child's expressed interests and preferred comfortable pace, with parents supporting, not pushing, the child. Learning which is dictated by parental interests and pace gives rise to terms such as "pushy" parents, tiger parents, helicopter parents, etc, and create a strong negative backlash. Children may develop a sense that they have no intrinsic self-worth but are only valued for their performance. Perfectionism, fear of failure, and procrastination are some of the possible negative results.

The goal of social interactions at this age may be to find the positives, strengths, and things in common with other children. Frequent comparison with other children may lead to negative traits such as being overly competitive, developing an interest in "besting" others, or using others as a foil to showcase one's own accomplishments,.

On this forum, where people understand the PROs & CONs of being gifted, one may freely share the accomplishments of their offspring. By contrast, in the world at large, there is strong alienation toward gifted children and their parents. In general, when others notice your child's accomplishments, be gracious and use the moment to create or strengthen a bond, rather than following a natural inclination to share your child's even more wonderful accomplishments and natural abilities. In other words, err on the side of caution and downplay it, until you are assured of the person's validation and affirmation for your child... rather than their weaponization of the child's differences.