6 months is definitely too young. Yes one can have a pup this age and younger out in the field with some very promising action but the dog is immature and it is for this very reason that bad habits are formed. It is my belief that unless obedience training isn;t properly ingrained, with constant stepping back at the first sign of trouble, and constant daily reinforcement of what is expected then bad habits will form. And once out in the field it is very difficult to back track to lesson 1. One is eager to carry on hunting, there are other distractions etc.
With regards to the killed bird I believe that yr pup is very keen. So keen that he killed the winged bird so it wont get away. I've seen it happen many times before. Chances are he'll deliver his next dead bird to hand perfectly.
Question: where there any other dogs hunting with you at the time? If he felt threatened by another dogs presence then it could be a reason why he crushed the bird.