All methods:
1. Use a plugin, Nodes as Tabs is free, already out of the question. *******'s paid plugin has a pure drop down option and it has the same problems as will be mentioned later.
2. Write your own plugin to add the extratab.
3. Put literally anything in the world you want in your template manually. HTML, CSS, Javascript all at your disposal.
Problems:
Pure drop down's are useless on mobile. When the menu collapses you end up with a non working link and no way to access the drop down. Id suggest making the tab link a link to a page also containing the links in the drop down as a stop gap. You won't like it but...
Any tabs added by code will be default use a split control for the drop down. You need to remove this in your template to make the whole navtab a drop down. This would effect more than just the one tab. Its a pain because by default the drop downs don't close and they have a delay so people end up clicking on the link trying to get the drop down to work. Need to override the default javascript to work around this.
Quick Link's isn't really anything other than a title. Your putting your own links in there so "just" quick links is whatever you define it as.
