we had a similar scenario but involving a rabbit which barkley managed to catch when he was 11 months old.
he had disappeared off into a thicket and the next thing i heard was a lot of squealing and he appeared a few minutes later with a very fresh, dead rabbit hanging from his mouth. my reaction was a bizarre combination of horror and pride!
'leave' is not one of barkley's favourite commands when he has found something really precious so i knew i didn't have a chance of getting it off him, so proceeded on our walk through the wood with a very cocky cocker proudly, but very gently, carrying his catch.
got back to the car wondering what on earth i was going to do, when luckily the situation was resolved as it became apparent that luckily barkley is more attached to me than a dead rabbit and so left it in a field when he realised i wasn't letting it into the car.
if the rabbit had been alive but seriously injured, i would have put it out of its misery. as it was dead, i left it for a local carnivore to benefit from. i wouldn't have taken it home.