There's really lots of things you could get. I went to a one year old's birthday party a couple weeks ago and liked that someone got her a personalized plate that she could keep for future birthdays. I also think a CD that you can add the child's name to songs is a really neat idea. Another idea would be getting the drum that has all the musical instruments in it. These are all gifts that I would want for my daughter, who will be one in four months.
Re: 1 year b-day gifts