We usually do that anyway
A friend and I never get together on each other's birthdays since she lives a couple of hours away. September is busy for her (she works at a University) and hers is in January and I don't travel out of travel much in winter because of weather-related reasons.
But MY birthday is and always will be a day that will forever live in infamy now. Oh, and what are the odds, the lady in the next cubicle to mine at work works with me in our 2-person section. Her birthday is also 9/11!