Well I don't want to be the barer of bad news but your child may be in for some daunting work. To do this experiment takes time, equipment (not usually found in your home), and a knowledge of organic chemistry. Also called the Miller-Urey experiment, this experiment uses an array of sterile flasks, glass tubes, and electrodes constantly firing for over a week to produce the desired result. You'd also need some of the chemical that would help to produce amino-acids such as... methane, amonia, and hydrogen, these materials can be found in easy enough to obtain products but they will not be experimentally pure. Plus you have to have pure H2O in order to conduct the experiment. Since we live in a world where you are not likely to find some amount of microscopic organic material inside the water unless artificially from pure hydrogen and oxygen in laboratory settings the experiment could be flawed.
But you know what, at 13 and with an interest like this is science I say give the kid the green light and set a budget for materials. Have him or her ask if he or she can use or even rent the schools science materials or if they can pick up the stuff cheap. If your child has the interest and the knowledge to conduct this type of scientific research it is better to give them support than it is to put a stop to it. My son and I made a comet using dry ice, window cleaner, soda water, rocks, dust, and soy sauce. You need a plastic bag, gloves, hammer, eye protection, and a mixing container. The thing actually out-gassed like a champ! These are some of the same basic materials and stuff found the experiment your child wants to do which is why scientists believe life may have come from comets hitting primordial earth! I hope your kid wins!