Running off to bed now, but what I would say is save yourself a ton of stress and DON'T MAKE THE CAKE! Unless you're a cake making guru (which I'm clearly not) making a first birthday cake is downright stressful and will distract you from what should be a wonderful celebration. Buy the cake.
Sorry if that seems a bit random but I think I would have enjoyed the day a lot more if I hadn't put myself under pressure to make a birthday cake that I felt was 'good enough' IYKWIM.