CUPCAKES! yikes they're SO easy, and so easy to make relatively healthy and all kids are thrilled by them (it seems). I often serve them at birthdays with whipped cream and strawberry sauce (on a plate!). I've used carob instead of chocolate, almond flour instead of wheat, rice flour, carrot cake, applesauce cake, nut butter frostings, etc... for my son's 4th birthday I made a cupcake volcano mountain with a vase full of strawberry sauce inside it for the lava and billowing whipped cream smoke and little silver balls (crappy candy, but very small) for ore treasures. It was a big hit at the party.
Also, don't underestimate what you can do with spirulina and beet juice as food colourings and little plastic animals from the toy store and edible flowers in season; whimsy beats out grocery store perfection any day. I used to make special order birthday cakes through a whole foods restaurant I cooked at and it was fun!
though really, I'm lazy, and for a 1 or 2 year old's birthday I would probably make fruit crumble with something creamy - our two year old wept desperately when we cut into his homemade winnie the pooh cake and refused to eat any of it (while looking at us like we were monsters).
Happy birthday to your little one!