Yes!
Most desert plants are pet and people friendly but there are afew which you should be aware of their toxic traits and take care of your pets, children and yourself in that regard. One example is the Crown of Thorns, which is toxic to both pets and people and its thorns should also worry you to avoid any injuries.
Barrel cactus' spines are extremely sharp and fierce, so good to handle with a lot of care to avoid any injuries.