A log like that is a good idea. I know that his sons took a great deal of comfort from it.
I've always wished I kept better notes. We party hunt here in Iowa so some years I kill five or six, some years I don't shoot at all, anywhere in between, no idea how many I've killed.
But I did find a neat little notebook at a local outdoor shop, "Rite in the Rain" all weather notebook. About 4" x 5 1/2", water resistant paper, fits in my back pocket, has plastic covers front and back. Been using one for a month or so for daily notes for work and play, every day in my back pocket, no signs of wear. Right next to it they had a "Hunter's Logbook". Same construction, just a little more specific in purpose and hunter orange covers. I'll be keeping better notes from now on.