Should I install a WDH?

Empty weight is irrelevant.  Gvwr is 7700, so figure 900-1000 hitch weight.  Is the max tounge with or without wdh?  Usually it's higher with wdh. At  best you will be pushing the limit if not exceeding it. 

Also what does the payload sticker on the door say?  Good chance you are over payload. Hitch weight counts against payload. Add in people and gear and you are likely north of 1500-1800lb. 

If you can keep within the ratings,  a wdh is a good idea.