Should you give protein supplements for a child that does not eat meat?

Maybe not. If they get protein from other sources such as milk, beans, tofu, yogurt, cheese, eggs, nuts etc. Then it is not necessary. Some children don't care for meat, but they can get their protein intake from other sources. A 44 pound (20kg) child truly only needs 20 grams of protein per day (about 1 gram per kg per day). You can check online nutrition websites for protein content of foods.
Amino acids. Need Amino Acids which is breakdown products of protein for body. A simple thing is to give peanut butter 1/2 tsp or almond butter will supplement protein needs.