http://www.animallaw.info/statutes/stusmsst97_41_1.htm#s1
A couple potential problems:
1) Your kitten isn't considered poultry or livestock. Fortunately, your state has a separate statute allowing the use of force to protect pets.
2) You shot at the dog after you scared it into dropping the kitten. The right to use force typically ends when the threat ceases. You could end up trying to convince a judge or jury that you were reasonable in your belief that the dog was still a threat.
3) You euthanized the dog. Most state animal cruelty law specifically authorize only police, the SPCA, animal control, and veterinarians to euthanize an animal.
Mississippi's statute is the first I've seen that allows ordinary citizens to put down an animal.
What you did appears legal in Mississippi but is not legal in all states.