Limited or zero eye contact
Do you have trouble getting your child to look you in the eye, or look into the eyes of other? Troubles with eye contact can often be a signal that autism may be present, and can be seen even in childhood. Lack of eye contact is said to be one of the earliest signs of autism, and experts very often include it in their diagnoses. There is still some discussion in the field as to why the lack of eye contact occurs mechanically, but it is generally accepted as a sign.
The Scientific American states, "toddlers with autism are oblivious to the social information in the eyes, but don't actively avoid meeting another person's gaze." So, it may not be that your child has a problem with eye contact, rather that those with autism are incapable of assessing the meanings behind certain looks, so they have no need to look into eyes like neurotypical people do.