2 mm of ABS was probably chosen for adequate stiffness and good surface finish. It also won't break if you fall off, as ABS has high strain to failure (it's likely to get a bit bent and scuff badly of course).
Modulus of ABS =~ 2.3 GPa (330 ksi).
If you use woven carbon (twill is quite pretty if it's bare with a surface ply of resin, but for a fairly curvy fairing you might find five harness satin easier to lay up) stiffness is going to be very roughly 50 GPa (7 Msi). Theoretically you could get the same bending stiffness as 2 mm of ABS out of 0.75 mm of carbon (bending stiffness goes with thickness cubed).
As PeterLester says, if you fall off then a carbon fairing is quite likely to break. You'll have to assess the likelihood of damage to you if so. If you're wearing leathers then the sharp broken edges might not do you too much harm.
It's also true that an aramid (Kevlar, Twaron, etc.) fairing would not be anywhere so likely to actually break in an impact (this is one reason that lightweight canoes are often Kevlar). For an aramid laminate with a carbon surface ply for esthetics the modulus would be likely to be about 3 Msi (20 MPa), giving a thickness of about 1 mm.
A hybrid of Kevlar and carbon might be good. There are some woven hybrids combining both fibres in the same ply. Oxeon's TeXtreme wide tow fabrics look pretty cool ( http://www.oxeon.se/