There are 13 colors, though I think it could be done with less without losing any information.
As for the picture, I would use the purples and dark blues to AA where the hat meets the black part (the face).
I would avoid dithering, as at that size, what you want is to put as much detail as you can, not blend colors.
The dark blue is too dark to put as inner oulines and shadows (at least IMO).
And well, add the mentioned characteristic features (the eyes, bigger hat etc).