"We do see some dogs where they do get sick from it, but there is some where it's just part of their normal make up," said Johnson. "If the pets aren't showing critical signs, then you can't even use how your pet is feeling with how to react."
Many experts said proper handling and storage of pet foods may prevent illnesses in some children. In fact, it may be as simple as keeping the pet food out of the kitchen, said Johnson.
"Certainly keeping pet food out of human food preparation areas will help," said Johnson.
But it may not be just the food's proximity to humans. According to Schaffner, young children should also stay away from the food bowl.
"The important thing is to try to keep very young children, those toddlers and those crawling around on the floor, away from the pet's food bowl," said Schaffner.
Schaffner also advised continually washing hands, washing the pet's food bowl, and washing out the water bowl after contact with any type of pet food to prevent illness.
"This is another little thing where we have to remember good hygiene is important," said Schaffner.
Johnson said he doesn't "think that there's a grave danger" for children if they are taught the proper way to handle their pet's food.
"I want people to still be able to enjoy their pets and think of them as their family," said Johnson.
Becker agreed, saying the overall health and wellness benefits of having a cat or dog far outweigh the possible risk of contamination.
"Reduce the risk, keep the pet," said Becker.
On "Good Morning America," ABC News Senior Health and Medical Editor Dr. Richard Besser also shared the following tips for keeping yourself and your family safe from salmonella:
Wash your hands after any contact with dry pet food.
Instead of reaching into the pet food bag with your hand or the food bowl, use a scoop that you use only for this purpose.
Keep pet food in a secure container -- not just in the bag, where it can spill out on the floor -- and away from human food.
While most pet owners feed their pets in the kitchen, consider doing it somewhere else, away from where you eat.
If you have a cat, be sure to wash your hands thoroughly after cleaning the litter box, because salmonella will live even after it passes through your pet.