I want to make a cookie stuffed with the cream filling you find in an Oreo. I've seen a few cookie sandwich recipes that use a filling made with butter. My question is, since this filling will be stuffed inside my cookie BEFORE baking, would the presence of butter cause issues while it's being baked?
A filling made with butter will melt at baking temperatures, and probably spill out of your cookies, or at the very least stop the cookie dough from baking properly (it will either soak the dough with moisture, break open the cookie with steam, or both) and not reform into the filling you want.
Instead, you should look into making hollow cookies and piping or injecting the filling once baked and cooled, or if you want filled cookies then find a recipe for filled cookies (but the filling will have to be something substantially different).