I am not aware of a native shortcut key unfortunately. I use the Saka Key addon which allows you to define a shortcut key for that and many other functions.

https://addons.mozilla.org/en-GB/firefox/addon/saka-key/

You can middle-click (or hold Ctrl and left-click) the Reload button on the Navigation Toolbar to duplicate a tab, that is what I use. To use the keyboard this would require two key sequences as you need to set focus to the location bar (Alt+D/Ctrl+L): Alt+D and Alt+Enter

cor-el, I did not know that you can open a new tab with the current tab's address simply by focussing the address bar then pressing alt+enter, so thanks, very useful.

One minor note, this isn't quite the same as duplicating a tab, as for one thing the newly opened tab won't inherit the current tab's backwards and forwards history. Not sure what else will not be inherited but then I am guessing that this is a non-issue for most. The methods you've outlined are certainly easier than using the tabs menu or installing add-ons, if all you want is a new tab with the same address.

To duplicate a tab along with its history you need to use the first sugestion with the Reload button. You can reach this button via keyboard navigation (focus tab bar location bar and press Shift+Tab one or more times).