Do I need to reinforce this joint?

Just glued up this stool for my nephew. Still have some cleanup sanding and other finishing to do, but wanted to crowd source some advice first.

I originally planned to join the steps to the frame with sliding dovetails... But screwed those up so they became dados. The wood is 3/4 inch thick . The steps weren't super tight in the dados and I just glued them in. I had planned to add some dowels, drilling through the side and into the step, to reinforce the joint. Now that I'm looking at it, it's super sturdy and holds my 200+ lbs. Would you add the dowels? All the weight is coming from the top, so is it even with it given the amount of surface that has glue? The dado is 1/2 inch deep.