We use molecular dynamics simulations to study structure formation in physically associating nanocomposite hydrogels. Nanofillers were modeled as rigid bodies of disk-like shapes and physical crosslinks were simulated by introducing a short-range attraction between the nanofillers and polymer chain ends. The structure, dynamics and mechanics of these polymer gels were studied as a function of nanofiller volume fraction. We observe the formation of a percolated network in the hydrogels, with an ordered local structure but disordered globally, as we increase the filler fraction. This locally ordered structure was a result of the anisotropy of the disk-like fillers. The dynamics of polymers showed significant caging effects in the gel state. Stress autocorrelation and elongation results were analyzed as a function of nano-filler concentrations. Comparisons with nanofillers of different shapes showed that disk-like nanofillers are more effective in strengthening the hydrogels than spherical nanofillers.