I forgot to tell my girlfriend I was leaving earlier on my birthday
Why would you not tell her is there a reason?
That's a dumb question.
It is good to tell people your plans before they happen. It is expected to let your partner know if you are leaving on your birthday.
It's okay because I'm going to end the relationship.
It is normal to forget things in the heat of the moment. If you were trying to catch her off guard to break up it might have just been better to tell her how you feel. She could freak out and it go badly.