The 'standard' Doomsday Argument hypothesis doesn't spend very much time on this point, and simply says that the reference class is the number of 'humans'. Given that you are human, the Copernican principle could be applied to ask if you were born unusually early, but the grouping of 'human' has been widely challenged on practical and philosophical grounds. Nick Bostrom has argued that consciousness is (part of) the discriminator between what is in and what is out of the reference class, and that extraterrestrial intelligences might affect the calculation dramatically.