May also come from the Tasmanian sheepfarming term 'to dag the hogget', i.e. to remove the testacles of a sheep by biting open the scrotum and sucking them out of the sack. After a day of this gruelling work one would be left covered in sheep's blood and faeces, leaving the person 'daggy'. See Errol Flynn's autobiography 'My Wicked Wicked Ways' for a graphic description of this practice.
My face and neck were covered in sheep crap after a hard afternoon of dagging the hogget. I was totally daggy.