Additional Subfloor Layer - Glue or Red Rosin Paper
If you truly want to add another layer of subfloor to the existing layer, you will only need to add another layer of 3/8" plywood, or OSB, (I am not a big fan of OSB) glued and screwed. THEN add the 5 lb. flooring paper, and your oak flooring. Otherwise I would go directly over the existing 1/2" subfloor with the flooring paper and oak floor. I suggest the lightweight tarpaper because it reduces moisture from rising into the floor from below, as in a crawl space. Red rosin paper, which I have used also for under wood floors but will no longer, holds moisture. It has been used under many floors over the years, I have demo'ed many floors that had it in place.

My reason for the littlest possible rise in the floor is it affects stairs, which become a safety issue,  doors need to be cut, and other things that need to be cut or adjusted from the additional height all the layers produce.