A firing pin like that is an easy job and a good one for a first school project. Drill rod is fine. 1/4" usually works OK for pistol firing pins, but check out 1/8 and 3/16. The smaller you can use, the better as there is less metal to remove.
IIRC, that is a pretty conventional firing pin, with a large diameter rear, a spring shelf, then a taper and straight piece to the firing pin hole. There is a standard cut for the retaining pin. I forget whether it is an inertia pin or not, but I would make it an inertia pin anyway. Make sure firing pin protrusion is right.
You don't actually need the old pin (though it helps) you just need patience and a fair amount of fit and file. If you have the spring, that helps too since it gives you the OD of the front part of the pin.
When everything works and you have test fired the gun, heat treat the pin and draw it. You don't want it too hard or it will be brittle (maybe the problem with the original).
Jim