we wondered the same thing for maggie's birthday last october. did not really do much, though the kids wanted to invite all the neighborhood dogs to a party. i couldn't bring myself to do that!
what I did do, though, is take lots of pictures through the day (we had a freak snowstorm so the pics were great), and that evening I sat down to write a "journal" as it would be written by Maggie, highlighting the past year and what we did for her birthday (we did make a cake for the humans to eat and we sang happy birthday to her. she was clueless).
Then I emailed the journal entry to her breeder because I am sure her breeder would love to read about how Maggie thrived her first year of life. our breeder was so touched by the email (and a few pics that i attached) she actually put it on her website for others to read (with my permission of course).
so if you are still in contact with your dog's breeder, I would be willing to bet that they would love to read about your dog's past year. i know my breeder said we were the only ones from that litter who did that, and it truly made her day.