>>Well, I'm not sure I'll go with animals. x_x I need something that's a little easier for me. <<

Plants would be another option.

>>Or... maybe because she can't have pets... she also collects stuffed animals and pretends they are real and talk to her.<<

That could work too.

>>Maybe it could be a stuffed animal her father got her before he was killed in a car accident. Like, something that she associates with her father and has a huge connection towards.<<

Good idea; it would help establish emotion in a character who doesn't display that in typical ways.

>>I wouldn't mind writing about the connection between Autism and having a 'friend' to talk to. But I'm not really sure.<<

So give it a try, maybe in a small scene. If it works, you can do more. If not, you can toss it and try something else.

Have you seen the way some folks are doing serials online these days? Some use strong continuity to tell a continuing story, while others are more like collections of related stories. I do mine in poetry, and you can see examples on the Serial Poetry page:
http://penultimateproductions.weebly.com/serial-poetry.html
kajones_writing does hers in fiction. Anyhow, you might consider something like that since you are exploring different aspects of a character and writing techniques that you might like to try. Doing new things in a modular setup of small ficlets would be easier to tinker with than a single longer story.