Cats have personal hygiene down to a science; their anatomy is made to perform all sorts of self-cleaning functions, and so most cats do not need regular baths like dogs. A cat's tongue acts like a comb with hundreds of tiny barbs that collect hair and particles as a cat licks his fur. A cat also uses his paws like a washcloth, licking the pads before wiping it over his face.
Most cats spend up to half their waking hours grooming themselves and any other felines (or dogs, or people) willing to sit still for it, which makes for a very thorough cleaning. Although you probably don't want your child spending half her day in the bathroom, your cat's grooming habits can be an example of how good hygiene is a must for all of us animals.
In addition to meticulous personal hygiene, cats can also be picky about how their meals are presented. Ask your child to be responsible for ensuring kitty's dining area passes inspection -- after all, she wouldn't want to eat out of dirty dishes, either.