No. I’ve never heard of chihuahuas being rodents, but they are small enough to be called a rodent if the child is not old enough to know the difference between an animal and a toy.
Chihuahuas are mammals because they nurse with mother’s milk, have fur, and five digits on feet (vs. four fingers for human hands) plus claws at the tip of toes which are especially for digging for food in burrows or earth. It’s always important to teach children about animals so that it becomes enjoyable instead of fearful. Visit your local zoo or animal shelter to learn more…