One approach that you might try is teaching your child how to handle inappropriate behavior by other children. First, don't let the child be a victim. Arguing or fighting will only escalate the situation. Responding with humor or ignoring negative behavior will be more effective. Of course, avoiding the child who engages in negative interactions is also effective, if that's possible. Some situations cannot be ignored, however.
Encourage your child to report such incidences to you or another adult she trusts. That individual might be a teacher, a coach in a sport, the principal, or a counselor. If the first person is unresponsive, you or your child should report the behavior to another adult in the situation. Be persistent in asking that action be taken.
Finally, realize that no person deserves to be treated rudely, to be made fun of, or to be treated in a mean way. Such behavior isn't about you; it's about the other person. And, you don't have to take it. Ask the person to stop. If they don't, take other action.
A second approach that I would suggest is creating opportunities for your child to develop good, solid friendships. If your child is gifted, her age may matter less than her interests and preferred activities. Look for play groups in your house of worship, through youth activities like the Boy Scouts or Girl Scouts, through community-based sports teams, through volunteer organizations, or even among children who live in your neighborhood, especially if you also have friendships with their parents. You may want to organize some outings with the families of other gifted children your child likes. Gifted students often need contact with other gifted children beyond the normal school day or week. You can find other opportunities through classes offered for gifted students on Saturdays or during the summer by local colleges and universities. Depending on the age of the children involved, these may be residential or day programs. Such enrichment programs can also meet your child's needs for additional stimulation beyond what is provided in school.