I'd be more concerned with him killing the rabbit than actually chasing it, although if as you say it was old and ill it's possible that the shock got it. I would make sure you watch him from now on though and don't let him get a chance to do this again, I wouldn't be walking him on ground where there's even a chance he's going to find game at his age. The best way to manage this is just to not let it happen, take him to places where you are the most interesting thing there - and make yourself the most interesting thing there! - so that he learns to focus on you for his entertainment.
He was probably still buzzing a bit from the rabbit experience which may explain his subsequent lack of interest in the dummies so again I wouldn't overly worry about that. Take him out again fresh tomorrow and see how he goes then. At just 4 months though I'd be limiting the amount of formal retrieving I'd be expecting him to do anyway, pups that age have the attention span of a gnat and get tired and bored easily. Do plenty of work on basic obedience and getting him bonded with and focussing on you - play with him, talk to him, keep his attention, use food (the only time I use food for training is in the early puppy stage when I dispense treats randomly to them as we go along), roll a tennis ball out for him every now and then, do lots of direction changes etc. Make everything into a game and make it fun and interesting for him. All this will help him learn to keep focussed and interested in you, it'll become a habit for him and then it'll make your job easier once you come to start his proper training as he gets older.