If your Notepad++ shipped with TextFX, you can find this in TextFX > TextFX Insert > Date & Time – short format, which will insert a string in the exact same format. If you don’t see a TextFX menu, install it via the plugin manager and it will appear.
You can then bind it to a keyboard shortcut in Settings > Shortcut Mapper… > Plugin Commands. Look for I:Date & Time – short format in the mappings.