The Red Dot FatBoy is pretty much a D1/F4 Toggle with the FatBoy twist to open knob.
This one is a D1 so made in 1958. The adjustment dial is 1 - 9 and the same as the FatBoys. The indicator is the Red Dot (as opposed to the little spring indicator) and is obviously how the nickname was derived.
The adjuster plate is notched.
Although extremely rare, there are some stamped F4 - so Q4/1960.

How does it shave?
It's about 2 settings more aggressive than the Standard FatBoy.