Navigating between pages

I have a page that displays a list of members from an API. Now, when a user clicks on a member (from the list), I’ve to load another page with that member’s details. Do I need a router for this? Or do I store data in the browser and when the user visits their details page, I get that data from the local storage and display it accordingly?

Note: I’m already using Vue but so far it’s everything’s been in the root instance and a component.