Hmmhmmhmm. I know this is Twilight fanfiction, and I generally dispporve of fanfiction. It tends to be sloppy, and done in an hour over a wave of enthusiasm.
But, I do admit, the first page is done okay. No, I'm sorry to say I can't tell you that its good, and it does need improvement, but that's why I review, hmm?

First off, your usign first person narrative because Stephanie Meyer did it, and you want to be a character in the story. That is the weakness of all fanfiction; the writer wanting to be in that world. I'm sorry, but get over it. Use what writing stlye fits you as the author, not you as the character.

Your narrative is awkward, people don't think like this. Memories are not blurs, especially memories of death. Don't whiz through it, I know your excited to get into the story, but we need to know the character. Tell us what happened to the parents, the sister (she would remember when she disappeared, not something like 'apporximately') and a little of her life with her aunt. 

In the orphanage, I don't understand why she is biased against, that phrase is super awkward and unneeded. Also, the younger a child is in an orphanage, the more likely they are to be adopted. People like raising children, and a teenager is the worst stage to have a child, so they want young kids, kids who are under ten, make this girl among the oldest, it'll really isolate her, and make the character stronger. When she meets Carlisle, remember that she has been interviewing all her life for a childhood, she's not going to be impressed by some handsome stranger, that's cheesy. He's a vampire, you have to explain that she has an unnatural attraction towards him, he's luring her in.

When she was in the car, I didn't feel anything. You threw emotion at me, you had her burst out crying. She's lived with this pain all her life, death and rejection. Don't you think she'd be numb to it by now? I think maybe its Jasper (I haven't read it, its not my thing) that does the emotion thing, so why is she crying?

However, you find a good place to close. We see you closing on the family, the one most of your readers remember from the original book series. And that's the problem; these aren't original characters, people already know who they are. I don't, but am I your target audience? If you do adapt the characters, people who have read the books will be mad because its not canon, and non-readers of the originals won't know who these characters were from the start.

Bottom line: Fanfiction is dangerous. I dislike it, because I like making my own characters, but this is your writing.

You have good focus, you can fix up your transition, and I think you do have a plot in mind that I hope you advance. I am actually curious as to why Carlisle chose her, and why he wanted a new vampire (other than that you want to be in the story dear). 

But I don't think 1st person is your strength, I suggest you introduce a twist to get out of it. Some metaphorical or psychologically breaking event to change the way people "view" your story. But really, you've done a good job, even though I don't read Twilight.

having written both my stories from multiple points of view, i suggest you refrain from explicitly saying things like:

"From Alice's point of view."

Instead try to make it clear through thoughts, conversation, surroundings, and the characters actions who is currently holding the point of view.

Just some friendly advice. :)

Just some friendly advice