No. Sure it's good for big apps to keep their store updated all the time, but also for small apps it's good. The implementation is easy for your usecase. One Endpoint in the store, one reducer and maybe 3 actions, and off you go. The ease of the implementation makes Redux also useable for small things. Because Why not? keeping everything clean is a nice goodie ;)
So basically: It's definitly no overkill, but for sure you could to small things without redux too. But then you can ask the following question too: Do i really need React for this App or could i simply use one Vue.js View too? (Which might be easier in this case).