You don't necessarily need DSC 1, but you will need the large game handling qualification which is one of the 5 parts of DSC 1.
You will also need to register as a food business with your local council. Much of it will depend on who you are selling it to and whether or not you are selling it in fur or skinned.
Sadly, you won't get much for Muntjac from a game dealer. I currently get £1.50/kg for muntjac, whereas I get £3/kg for Roe!
MS