No, it's not a Stanley No 1, but it is probably one of the nicest versions of one of the all-time-great eggbeaters --- The Millers Falls No 2.
Yours is an earlier model, with one pinion gear and a little thrust wheel. It is far smoother-running than the later, 2-pinion models.
You can read a lot more about that thrust wheel (George calls it a "LRRCW") over at George's basement.
Judging from the star logo on the handle, I suspect yours is pre-1921 -- probably the late 19-teens.
I haven't checked the auction site lately, but a few years back, those got really popular and fetched 80-90 bucks. I must have sold six or seven and kept only my two favorites.