I too have heard about the oats debate. They supposedly have gluten in them because they are so closely grown to wheat. There are places online to get gluten-free oats. This recipe is a favorite from my childhood. My mother made these often. Thay are so easy to make, yet so hard to stop eating!
Just a quick note- There is currently debate over oats being gluten free. In Australia the Coeliac Society are not recommending oats as part of a gluten free diet. They are however, wheat free. Your recipe looks like a good one!
I added coconut and walnuts to the recipe and it turned out great. Very sweat cookie.
I should have also mentioned, I have not found gluten-free quick cooking oats. Maybe they are out there. Also, recipe should mention peanut butter in title.