^SM is right. They don't ask for any sort of ID, so everything should be fine! I went to Disneyland 2 days after my birthday and although it felt weird for people to say "Happy Birthday!" when it wasn't *exactly* my birthday, it was still cool since I did nothing on my actual b-day.
Sometimes I think they *should* ask for ID because there have been some times when I see an unusually high amount of people with birthday stickers. I know that many people couldn't all be born on the same day AND come to Disneyland on the same day!