Identifying Arne Jacobsen dot hocker stool  

It really doesn't look like one. If you want to check by yourself, "FH made in denmark" should be embossed in the wood under the seat.

It's not FH.  As far as I know, the Jacobsen stool was only produced with three legs and not upholstered.

I agree, it's not Jacobsen. The dimensions are way off.
However, the stool "dot chair" (model 3170) is nowadays only produced with 4 legs by Fritz Hansen.
Jacobsen designed the dot chair alongside his work on the ant chair (3100) in the early fifties. Both chairs were designed with 3 legs.
Fritz Hansen altered this in 1970, where they "updated" the dot chair to 4 legs, while the ant chair became available in both a 3-legged and 4-legged (3101) version.

I_love_danish, thanks for clarifying. 4-legged stools usually look weird to me.

@woodywood
I agree. There's a reason why Jacobsen designed it with 3 legs. It goes for design as well as for cars. Don't fix it, if it ain't broke.