Ya' know, I think most mindful mom's bump into this and I feel like the most popular 1st birthday cake is a vegan carrot cake. Seriously, I think I know about 20 kids who had this for there first birthday cake. heheh...
If you're interested I have a great vegan cookbook named "How it all Vegan". I know that there is low-sugar egg and dairy free recipes for carrot cake, chocolate, vanilla etc...there are probably a few variations of each.
They are all good. I've made them with a whipped banana filling (also, from the book). It's all pretty good and healthy.
I think people understand that a one year old has special diet needs and seeing that it is there birthday - the cake should accommodate them.
If you are interested in some recipes, or any one in particular, please let me know and I'll e-mail you some recipes.