I'm going to drop her on her birthday
Why would you wait until your birthday?
I want to have fun on my birthday, which is the same day, so I have to drop her
You should think of your girlfriend's feelings as well: she wants to have fun on her birthday just as much as you do, but she wants to do it her way.  You shouldn't give bad news to a close partner on such an important day.  If you care about her, maybe you could take turns with your birthdays, or celebrate on different days.
Nah, I think I'll be happy with all that drama.
I think that you should really just wait until the following day. No one wants to get bad news on an important day like that.