For an “activity” at my son’s first birthday party where the guests were too little to do much of anything we just made up a “birthday parade”. We had all the kids lined up holding balloons, party hats on, etc. The birthday boy was in front pulled in his wagon and the others behind walking or in strollers, whatever.
We just had a tiny little parade, played music, took cute pictures, hollered “Happy Birthday!” clapped, and gave candy and prizes to the guests. Oh and also for the adults I fixed a poster board with lots of cute pictures of baby and family members showing scenes from his first year. Barbara