By default, all web hosting accounts have only one shared IP address and no dedicated IP address. You can find your site's current IP in the left hand menu of the main page of cPanel.
A dedicated IP change requires 4 hours to resolve. Your site may appear to be down during that time. You will NOT need to change your name servers.
If you choose the dedicated IP, all of your addon and subdomains will use the dedicated IP. Emails will still use the shared IP.