We study the dissociative ionization of water clusters by impact of 12 MeV/u Ni25+ ions. Cold target recoil ion momentum spectroscopy (COLTRIMS) is used to obtain information about stability, energetics and charge mobility of the ionized water clusters. An unusual stability of the H9O4+ ion is observed, which could be the signature of the so-called Eigen structure in gas-phase water clusters. From the analysis of coincidences between charged fragments, we conclude that charge mobility is very high and is responsible for the formation of protonated water clusters, (H2O)(n)H+, that dominate the mass spectrum. These results are supported by Car-Parrinello molecular dynamics and time-dependent density functional theory simulations, which also reveal the mechanisms of such mobility.