  We analyze the full transport statistics of graphene with smooth disorder at
low dopings. First we consider the case of 1D disorder for which the
transmission probability distribution is given analytically in terms of the
graphene-specific mean free path. All current cumulants are shown to scale with
system parameters (doping, size, disorder strength and correlation length) in
an identical fashion for large enough systems. In the case of 2D disorder,
numerical evidence is given for the same kind of identical scaling of all
current cumulants, so that the ratio of any two such cumulants is universal.
Specific universal values are given for the Fano factor, which is smaller than
the pseudodiffusive value of ballistic graphene (F=1/3) both for 1D (F=0.243)
and 2D (F=0.295) disorder. On the other hand, conductivity in wide samples is
shown to grow without saturation as \sqrt{L} and Log L with system length L in
the 1D and 2D cases respectively.
