Understanding the elusive catalytic role of titanium-based additives on the reversible hydrogenation of complex hydrides is an essential step toward developing hydrogen storage materials for the transport sector. Improved bulk diffusion of hydrogen is one of the proposed effects of doping sodium alanate with TiCl3, and here we study hydrogen dynamics in doped and undoped Na3AlH6 using a combination of density functional theory calculations and quasielastic neutron scattering. The hydrogen dynamics is found to be vacancy mediated and dominated by localized jump events, whereas long-range bulk diffusion requires significant activation. The fraction of mobile hydrogen is found to be small for both undoped and doped Na3AlH6, even at 350 K, and improved hydrogen diffusion as a result of bulk-substituted titanium is found to be unlikely. We also propose that previously detected low-temperature point defect motion in sodium alanate could result from vacancy-mediated sodium diffusion.