Ask her, especially about the cake. The card and gift can be passed off as "Oh, I was walking through the store and saw these and thought of you," but a cake comes across - to me, at least - as a bit more involved.
I'd love it if I was able to keep my birthday a secret, but I end up being put on the spot every year and it makes me incredibly uncomfortable. I've never been asked if I wanted it or not, it was just shoved on me because it was what they wanted. (When it comes closer to my next birthday, I do plan on shining my spine and putting my foot down as much as I can, but I still have a few months.)