  Future radio observations with the SKA and its precursors will be sensitive
to trace spiral galaxies and their magnetic field configurations up to redshift
$z\approx3$. We suggest an evolutionary model for the magnetic configuration in
star-forming disk galaxies and simulate the magnetic field distribution, the
total and polarized synchrotron emission, and the Faraday rotation measures for
disk galaxies at $z\la 3$. Since details of dynamo action in young galaxies are
quite uncertain, we model the dynamo action heuristically relying only on
well-established ideas of the form and evolution of magnetic fields produced by
the mean-field dynamo in a thin disk. We assume a small-scale seed field which
is then amplified by the small-scale turbulent dynamo up to energy
equipartition with kinetic energy of turbulence. The large-scale galactic
dynamo starts from seed fields of 100 pc and an averaged regular field strength
of 0.02\,$\mu$G, which then evolves to a "spotty" magnetic field configuration
in about 0.8\,Gyr with scales of about one kpc and an averaged regular field
strength of 0.6\,$\mu$G. The evolution of these magnetic spots is simulated
under the influence of star formation, dynamo action, stretching by
differential rotation of the disk, and turbulent diffusion. The evolution of
the regular magnetic field in a disk of a spiral galaxy, as well as the
expected total intensity, linear polarization and Faraday rotation are
simulated in the rest frame of a galaxy at 5\,GHz and 150\,MHz and in the rest
frame of the observer at 150\,MHz. We present the corresponding maps for
several epochs after disk formation. (abridged)
