Pretty much any cat will make a good mouser. If mice are available, a cat will hunt them and it doesn't really make a difference what temperament the animal has, he will try to hunt mice. So the main thing for you to consider is how laid back and easy going the cat is. Children tend to 'maul' cats a lot. They hug too hard, they pull tails and they just basically do everything that annoys the 9 lives out of most cats. But there are cats out there who don't mind when little ones do such things and would even fight to the death to protect that child. So look for a cat who doesn't frighten easily, acts calm no matter what you do, and is not alarmed at the very sight of your child coming at him. Any cat breed can produce such a kitty so all you have to do is look around. If you are allowed to pet the cat in question and interact with him before adopting him, so much the better. A cat who purrs readily and looks happy to have you around is a good choice. On the other hand, a cat who jumps back, grimaces or looks startled is a poor choice. If he runs and hides, or growls when you touch him, then he is not a good idea for a child's pet. Make sure also, that you pick a kitty who is strong and healthy. If his fur looks matted and greasy, that means he is not grooming himself and that's a sign of illness. If his eyes are watering or he's coughing a lot, those are also signs of illness. If he scratches at the same ear a lot, he probably has ear mites and those will irritate him until they are treated and that will make him irritable with your child as well. So... healthy, strong and happy are key. Definitely choose the most laid-back cat you can find.