The duplicate functionality you're describing does not exist in XD. However, the easiest two options for easily duplicating objects are the Repeat Grid feature, and using the Alt + Shift shortcut.
Select the object and then enable Repeat Grid (Ctrl + R). Note that items in the repeat grid are linked, meaning that any change to an object within the repeat grid will also apply to the others.
Alt + Shift
Hold and drag the object while pressing Alt + Shift. If you're working with more than 2 objects that require the same padding/margin, you will see helpful guides that let you snap to the same spacing. I personally find this method to be the fastest and most efficient.