Oats do not contain gluten.
"Gluten is a special type of protein that is commonly found in rye, wheat, and barley. Therefore, it is found in most types of cereals and in many types of bread. Not all foods from the grain family, however, contain gluten. Examples of grains that do not have gluten include wild rice, corn, buckwheat, millet, amaranth, quinoa, teff, oats, soybeans, and sunflower seeds."
Google the word gluten and look at the second article.
Make your own applesauce and cooked carrots. Process it into toddler food. Do the same with cooked meat. Your child can eat anything you can if you process it after you cook it. And it is better for him as it does not include food stabilizers or chemicals you cannot pronounce.
I ruined more than one cheap processor trying to do for a spouse that has a special diet. I finally bought a professional unit and the companion chopper. Do not feed your child corn as there is zero food value in it because the human stomach is not ruminat.
You can process any meet, veggie and fruit at home into a food your child can easily eat. And you can make your own bread.
My girl has a lot of food allergies. I spent considerable time learning. I kept all the information in a Food Allergy list. I will post it in this forum.