Very few baked products at WDW are considered to be allergy nut free safe. They may not contain nuts, but most have a trace or same factory or line warning. I have heard that the ones at BOG are nut free safe, but we have not been there yet, and have no conformation of that.
There is a bakery in DTD called Baby Cakes that does allergy friendly baked products. There was some question about them being completely 100% safe, but we are good with their policy.