Even in the few GeV2 region, there is already a pronounced deviation of the nucleon form factors from dipole parametrization and scaling. With the pion cloud model of nucleon structure formulated in the light-cone Fock approach, the Q2 dependence of all four elastic nucleon form factors Gp,nE (Q2) and Gp,nM (Q2) is examined. Two different mesonic effects are included: the coupling through intermediate vector mesons to bare nucleons and the direct photon-pion interaction with pion-nucleon and pion-delta components in the nucleon. Contributions to the physical nucleon form factors from various sectors of the model space are calculated and compared. The model predicts scaling violation of roughly 10% which is consistent with perturbative treatment of the π-N and π-∆. The observed deviations from dipole parametrization are attributed to pion cloud at small Q2 and perturbative quark-gluon dynamics at large Q2.