I am sorry to hear about your dad. That must be an odd feeling that your life is moving forward while his has now stopped.
I think birthdays are a fine time to feel sad if you want. There is a lot to take in, including missing people that are not longer part of our journey.
Of course, the other side of that coin is remembering how they made our lives better, and opening ourselves up to appreciating the love we have right now. For the very reason that life moves forward and things change, and if we don't appreciate what we have, we miss it.