The structure and dynamics of potassium chloride in aqueous solution over a wide range of concentrations and in particular beyond saturation are studied using molecular dynamics simulations to help shed light on recent experimental studies of nonphotochemical laser-induced nucleation (NPLIN). In NPLIN experiments, the duration, t, of the laser pulse (with wavelength 1064 nm) is found to influence the occurrence of crystal nucleation in supersaturated KCl(aq): if t is less than about 5 ps, no crystal nucleation is observed; if t is greater than about 100 ps, crystal nucleation is observed, and with a known dependence on laser power. Assuming that the laser acts on spontaneously formed solute clusters, these observations suggest that there are transient structures in supersaturated solutions with relaxation times on the scale of 5-100 ps. Ion-cluster formation and ion-cluster lifetimes are calculated according to various criteria, and it is found that, in the supersaturated regime, there are indeed structures with relaxation times of up to 100 ps. In addition, the ion dynamics in this regime is found to show signs of collective behavior, as evidenced by stretched exponential decay of the self-intermediate scattering function. Although results do not explain the phenomenon of NPLIN, they do provide insights into possible relevant dynamical factors supersaturated aqueous solutions of potassium chloride.