  In this paper we define a Weil-Petersson type metric on the space of
shrinking Kaehler-Ricci solitons and prove a necessary and sufficient condition
on when it is independent of the choices of Kaehler-Ricci soliton metrics. We
also show that the Weil-Petersson metric is Kaehler when it defines a metric on
the Kuranishi space of small deformations of Fano Kaehler-Ricci solitons.
Finally, we establish the first and second order deformation of Fano
K\"ahler-Ricci solitons and show that, essentially, the first effective term in
deforming Kaehler-Ricci solitons leads to the Weil-Petersson metric.
