Gerbils do make excellent pocket pets for young children. While I do not recommend that any child under age 7 or so be the primary care-giver for any animal, young children can care for gerbils with adult supervision.
Our four year old and two year old enjoy feeding the gerbils each day, and since gerbils naturally forage for their food, it doesn’t matter whether the kids get the food in the food bowls or not. Our gerbils enjoy the hunt regardless!
Gerbils are quick, however, so it would be difficult for a small child to hold a gerbil by themselves. We let our kids sit on the bed and hold their hands open in their laps. The gerbils, naturally inquisitive, are only too happy to walk across their open palms, “tickling” their arms. The children have been taught to hold still while the gerbils walk on their hands and arms, so the gerbils do not get accidentally squished by an overanxious child.
Older children can tend to a gerbils basic needs of food and water with ease. Changing the bedding only needs to happen once or twice a month for many gerbils, since the rodents are desert natives and produce little urine.
See additional resources for gerbils and children on Amazon.