As an alternative to the usual turtle or hamster, you might want to consider getting your child a walking stick, one of the most popular insects to keep as a pet. They can hide in plain sight with camouflage that is so perfect they are nearly indistinguishable from the branches of the plants on which they feed. Blow on them and they will even sway back and forth on their long legs to mimic the movement of a twig in a breeze.
There are almost 3,000 species of stick insects (or phasmids) worldwide. Perhaps the easiest to care for are called Indian, or laboratory, stick insects, Carausius morosus. They have the habit of folding their legs in when held to complete their stick disguise.
Although most species are long and slender, some of the more spectacular varieties have flattened bodies and disguise themselves as leaves. One of the most impressive of these is the Australian spiny leaf, Extatosoma tiaratum, which can grow to resemble an 8-inch-long spiny branch with dead leaves for legs.
You or your child may pick up the stick insects and watch them crawl about. The major concern is that the animals may injure their delicate legs. They can hold onto things with a pretty good grip, and some would prefer to lose a leg than let go. Some of the large spiny varieties can also pinch with their thorny legs or bite. One, the American walking stick, Anisomorpia bupestroides, should be avoided. This insect, which has two stripes on its back, can spray an acidic compound that has been reported to cause temporary blindness.
For more information on these pets, see the story Choosing a Stick Insect