I love
Alice too (my great-grandmother's name was
Alice) but I don't know if I'd use it right now because of the Twilight Book series. It might be seen as coming from Twilight, so I don't know if I'd like that.
However, I would still encourage you to use it if you really like it. I don't think it's too dated, I knew a girl who would be 18-19 now who's name was
Alice. My great-grandmother had a sister close in age who's name was
Audrey. I really like it as a sibset :)