Since I used a white coloured coat of the mini Mex, I had to experiment with some settings and lighting, because the skin colour was shown through the coat.
I had to increase the children to 20 and set Segments and Seed both to 5, also setting Kink to Spiral, for experimental hair grow on the rabbit.
And finally what made the white colour of the furr come out best was changing the background colour from standard grey to bright white, thanks to an old tip from Mike in the Q&A.
These settings made my computer compute very hard in producing the render, over 15 mins, whilst I think the 35thousand Tris had also a little contribution in the calculations.
Perhaps in a later stadium I will decimate my rabbit mesh to lower the tris count?
I tweaked more settings resulting in this render: