You don't need to use any plugins. Quark is already using the Font Awesome icon font to display the social links that you see in the header. As you would've no doubt seen, you can set the url's for these social icons in the Theme Options page.
If you simply want to replicate the icons that are in the header, exactly as they are, but in the footer, then you can simply call the function that I created.
If you have a look in header.php, you'll see the following...
<?php echo quark_get_social_media(); ?>
If you copy those couple of lines and add them to your footer.php template, it will output the icons exactly as they appear in the header. If you've created a child theme, then simply copy the footer.php file and add it to your child theme folder, and then add those three lines of code wherever you want the icons to appear.