Hi S.. For my daughter's first birthday party I made a carrot cake (I'm sorry, I don't remember which recipe I used, but I did cut the sugar in half, and added some beet juice and raisins for color and vitamins). I made a cream cheese frosting, again cutting the sugar and adding beet juice so it would be pink. My husband did simple lettering. It was a great cake, and everybody was happy since it was relatively healthy (parents) and tasted great too (parents and kids)! Some of the parents had two or three helpings :)
We kept our party simple, a gathering of four of her friends and their parents and 4 or 5 of my friends and "honorary aunties" down at a local park where it was easy to get a picnic table and there wasn't a lot of traffic. At one year, my daughter was more interested in taking off the paper from her presents than the presents themselves, and it was great for the kids to be able to run around in the grass and play on the play structures in between party activities.
Good luck, don't stress, and have fun!