Does my cousin have Asperger's?

I have been watching my younger cousin closely lately. She is fourteen years old and will turn fifteen at the end of October. These are things I have noticed about her:

-She has an obsession with The Lion King

-Although she does not choose to watch it, if Thomas the Tank Engine is already on she will watch it without complaint, seemingly interested. She likes the theme tune.

-She is in her own little world a lot of the time. She likes to be on her iPod listening to music or on her laptop or reading a book and not talling to anyone. She gets very upset if someone is to take her iPod away from her and seems very anxious without it; I have come to the conclusion that she finds comfort from having it with her.

-She is incredibly socially awkward, scared to go near strangers however much we encourage her to make new friends. She dislikes physical contact and avoids eye contact unless she deeply trusts you. She hardly ever initiates hugs and although claims to like hugs, pulls away as though frightened when you hug her. Although, once you make friends with her she is very loyal and gets attatched to the person- if that person was to die or move away for example, she would pretty much break down.

-She is in top set for everything at school, often achieving high average or above. She gets brilliant Math results although she complains of a headache when doing math problems, and despite claims of trying very little and not being interested in the sciences, gains way above average marks for it.

-She excells at drama and drawing, and has her own little world she 'visits' and makes stories with.

-She still has imaginary friends.

-She has very high happy days and then days where she is grumpy, snappy and seems sad.

-She has problems speaking about problems with people and expressing her feelings.

-She can get very hyperactive at random times for absolutely no reason at all.

So, what do you think? Thank you :)