I understand your anxiety and let me start by saying what a wonderful parent you are for doing your research, but from everything you described I don't personally see Autism of any sort but more a gifted child. I have never heard of a doctor zoning in on a child reading and declaring Aspergers. I would definitely seek a second opinion. Also look at the following link:

http://www.hoagiesgifted.org/special_needs.htm

Big hugs to you ... but really the only thing that stands out in your post is the parallel play and that too can be part of gifted and social issues.

I am sure you will get more advice on this board ... there is a lot of parents with 2E kids (Twice Exceptional) who have had to go through similar things.