I'm pretty sure her birthday is November 9.
There's this art by Kei-san that says the date for her birthday is 2013.11.09. Also, there's this twitter post where she thanks Okiku and Giga for their presents. It's dated Nov. 8 but it was Nov. 9 in Japan when she uploaded it.
I'll be using the pic as source~ thx >.<
What do you think?