If you are in the US, the school district has to help you assess. The eye contact issue is a red flag for Asperger's and other autism spectrum disorders, but also for problems with ocular motor control and visual processing, all of which respond best to early intervention. How difficult this assessment will be in terms of what resources are close to you and which ones require travel is another question. Speaking as the parent of a gifted child with all of the aforementioned diagnoses, I don't think there is a down side to having this checked out by knowledgeable professionals. If there is a problem, then you can begin to offer interventions early to help build skills, and if there isn't a problem, then you can stop worrying.