Whois button will appear when domain unavailable. To enable this function, you have to create new page for the Whois page, you can create new page with whatever title you want.
eg: “Whois” or “Whois Domain”. Make sure this is page not post.
Then, put shortcode on the page and then go to WP Domain Checker settings, on Whois Page section, select page you created before.
Select disable if don’t want to show the Whois Button.