I believe your early Model D's used a Davis long needle and the later ones used the common 15x1 found everywhere. You can check to see if it's the Davis long by measuring an existing needle that sews and it should be a little under 2". For occasional sewing a tube of Boye 10 (NOS) needles from ebay or perhaps someone will have some for sale from the QB will work. For frequent sewing I'd recommend MTx190 industrial needles which are slightly different (round instead of flat on one side) than the originals but do the job and are inexpensive. I have a later "D" which is motorized and in a bentwood case and uses 15x1's but the needle size is marked on the front slide plate.
Very cool to have a 100 years of family history in your NF Beacon.
Jon