First of all, you don't need to dye your hair black. I wouldn't recommend it as I did the same thing about a year ago and it just made me look really sickly pale, not elegant. If you DO want to look a little bit more pale and pull off a great Alice Cullen costume here is what I would suggest:
Find a foundation about a shade lighter than your actual tone. This doesn't mean go out and buy the whitest make up you can, but using a color that is a shade or two lighter will give off the illusion that you are pale and by covering the foundation (liquid) with a similar colored powder it will give the illusion of evenly colored and nearly flawless skin (depending on if you have blemishes or not).
Your hair should be flipped out or you should use gel to spike it. Are you being the Alice from the books or movies? Alice in the books has a pixie cut, which is actually a style too short to curl out and she uses gel or glue to kind of spike it a little. Don't go crazy with it, just remember that the goal is to look elegant not intense.
If you're looking for a good costume the book mentions that she mixes together punk and victorian fashion, and the movie is a good reference for that. Her outfits are not impossible to get. The best costume would be a simple dress (anything from a place like Maurice's, American Eagle, and Forever 21) that reaches just above your knees with leggings, flats and a light knitted wrap or thin knitted jacket. I forget what they're called but there aren't a ton of knitted jackets so I hope you know what I mean. Grow your nails out a bit and paint them with clear nail polish, be sure to keep your cuticls neat and trimmed. Wear nice earrings and a bracelet or ring. Your blush should be very light and used only on your cheek bone and try and use a light shade of lipgloss as well.
Use an eyelash curler and defining mascara to give your eyes a little boost and white eyeliner to make them shine a bit more. If you want you can also buy yourself gold contacts online to mimic Alice's vegetarian side effect, or red ones incase you're wanting to be a hungry Alice.
DO NOT buy vampire teeth. Remember that in the story they do not openly have fangs, they have caps in their teeth.
Note: As far as the costume goes you don't HAVE to wear the dress. Remember that Alice is very fashionable and go to your local mall or dress stores and look at the manicans. Anything that they are wearing is probably what Alice would put together for either herself or Bella.
I was Alice in a Twilight Cosplay contest at our theater.