My two are great chasers of leaves and flies, and love chase and catch games with a feather on a string, but neither of them have ever caught and killed anything. They are 2 years old and 11 months old. The older one brought in a live mouse once but I genuinely think she thought it was her friend, and to be honest the younger one is similar, he thinks everyone is his friend and was trying to get my 4 week old niece to pat him 
I love the way they are but will they ever change? Did yours start bring dead things in at a particular age?