Using the vue-auth plugin with Vuex is just a matter of routing all the calls through a store. It's best to take a look at the demo auth.js store file for an example of this.
Not much else to really cover here.
Only thing to point out is that the vue-auth plugin already maintains it's own state for the user object so duplicating it via a Vuex store doesn't really change much. The main advantage of using the store is to centralize the logic which is useful for having consistent handling of various functions like login and register.
Also, at some point the app may introuduce some form of subscription sign up. This will also increase the complexity of things so better to have that logic centralized than scattered around in components.