A: A steady peg dog that is not used to this new situation may react in the same way as any young dog. I have experienced the same thing with a young labrador, which refused to pick the first winged bird, but subsequently became proficient with all wounded game.
Your dog will obviously be very steady to game and the first pigeon may not have looked as though it was winged.
Your dog needs to be well behaved on a formal shoot and has learned from experience to ignore any unshot game walking past the peg.
If it happens again, which I doubt, then immediately catch the bird, kill it, put it down and then send the dog back to retrieve it. Once he is confident he is doing the right thing, this should not occur again.