For my daughter's first birthday, I ordered a fondant cake ( I think it was just sponge cake under with cream) along with a dessert table which was more meant for the guests and family members, but my daughter also enjoyed her first bites of cake (just the sponge and cream, no fondant). Unless your little one has dietary restrictions, I think it's okay for them to have a few bites of their cake.
for my girl birthday, we ordered our cakes from pine garden, and I only let her eat one small mouth of the sponge cake part, avoiding the cream, although mine is just a normal plain fresh cream,
Is their birthday, so I think is nice for them to have at least one small mouth