I agree that it makes sense to have your district evaluate. Write a letter describing your concerns and they MUST evaluate in all areas of suspected disability. If she has trouble with certain social skills, behavioral regulation, flexibility, language, motor skills etc mention these things in the letter. Even if she is at grade level or beyond, she may qualify for help in other realms such as social.
As far as the eye contact - yes it is a red flag for Aspergers and other spectrum disorders. People with ADHD also sometimes with eye contact. From what I have read, it actually helps them to concentrate and block out extra stimuli by looking away. Perhaps you can help your daughter understand when eye contact is essential and let it go when it is not important. It may make her concentrate on other aspects of human relation and conversation that is more salient.
