Ah, got it. What about piping Power Query into Power Pivot? Then you could use the Duplicate button.
Or, even better, use the first query as the source for a second, third, fourth, etc. query which should allow you to change the first query and have it automatically affect the other queries.
You can customize names and add calculated columns with Power Query, but you can't do measures. But measures aren't table-specific in Power Pivot anyways though so that shouldn't matter.
This might be a silly question, but are you sure you even need to duplicate the Date table? Many times you can get away with connecting all your other tables to just one date table.