Could my 2 year old have Aspergers Syndrome?

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I am adopting a 2 year old who I have had since she was 12 days old. She was born 9 weeks premature yet she started walking at 10 months. She walks on her tip toes and has been diagnosed with "abnormal gait". She is very smart.  She talks very well. I am worried because her mother and father both have significant mental health issues such as bipolar disorder, schizophrenia, psychosis, and manic depression.  For the last 6 months or so my child has had some behavioral problems. She is really agressive to other children.  She will run across the room and hit a child with a toy. She pushes. She bites. She pinches and scratches... these all sound normal for a 2 year old except she does it for no reason. She will be content one second and then lash out the next. My cousin had a 9 month old and my little girl always runs up to him and pushes him down then she grabs his hair and smacks it into the floor.  This is a repeat offense. She will do it every time she sees him.  She also grabbed onto my other 2 year olds face and wouldn't let go until she was bleeding. She also bites herself and smacks her head into the wall.  She doesn't bite herslf once, she will do it all over herself.  She is also clumsy, she walks with a bounce.  She is very good at legos and blocks and she is always writing with a pen. She is obsessed with writing. Any answers and opinions would be helpful.