You have the diameter right, though this should be considered a target diameter, or optimum size, as precision is a bit elusive when working this close with a lathe, as most people will be doing. I always put a taper for flaring the case mouth, rather than a step as in the Lyman M die. I like the taper best because one can adjust the amount of flare needed to prevent lead shaving when seating bullets, and not overwork the brass at the mouth as a fixed diameter which is well over mandatory size would do. This to give maximum case life before the necks split. I hand file a nice radius on the starting end, in the lathe, after turning to final diameter, and cut the taper which will flar the case by either setting the turning tool to the desired angle so the final cut leaves the taper, or use the compound set at 30 degrees, so the taper is gentle. Polish the part well in the lathe after turning, as doing it after heat treatment is difficult if the maching isn't real smooth.
Best material for making expander plugs is oil hard tool steel, which is available from steel suppliers. Lathe turn the part, heat to a dull yellow, quench in oil until the part can be held in the hand. Draw by warming gently until oil on the part smokes when the torch is removed. (About 450 deg F.) Allow to cool to room temp and draw again.
Warm gently means hold the acetelene torch back from the part, with a fairly low flame, so the heat doesn't come up too rapidly. Drawing is mandatory to prevent the part from cracking some time later. If you purchase water hard drill rod, only one draw is needed, and ideal draw temp is 400 deg to retain maximum hardness. The double draw is mandatory for oil hardening tool steel because it goes through a secondary hardining cycle at room temperature. You don't need to understand all the tech details so long as you just draw twice.
Water hard will shrink .002 per inch of diameter, so allow a bit more than .001 oversize for this shrinkage. Oil hard expands very slightly when heat treated, so the part can be cut to almost the exact desired diameter before heat treatment. With either, polish to final diameter after the part is hardened.
