Customizing menu link output (add badge)
This is the function you'll need:
https://api.drupal.org/api/drupal/includes%21menu.inc/function/theme_menu_link/7

That allows you to overwrite the standard theme function. You could do an if statement to check for that specific menu link ID and do a custom output. 

You'll need to put that in template.php within your custom theme and replace "theme_" in the function name with the name of your theme