Many ABX₃ perovskite compounds adopt at temperatures of interest a low-symmetry structure, rather than the ideal (cubic) structure. The prototypical case is the mineral perovskite (CaTiO₃), which exhibits orthorhombic symmetry over a wide range of temperatures, attaining ideal, cubic symmetry only at very high temperatures. In this study, we made use of this behaviour to examine the effect of crystal symmetry on oxygen diffusion in a single perovskite material. Employing molecular dynamics (MD) simulations, we calculated oxygen tracer diffusion coefficients in CaTiO₃, doped with various acceptor species, in the range 1000 ≤ T/K ≤ 2500. The activation enthalpy of oxygen tracer diffusion was found to be larger for the orthorhombic structure (0.58 eV) than for the cubic structure (0.43 eV). In addition, oxygen tracer diffusion was found to be adversely affected by the presence of acceptor-type cation defects, with stronger effects being observed for the low-symmetry structure. Our results also allow us to suggest explanations for the large scatter observed in experimental transport studies; to derive trends for the alkaline-earth perovskites; and to emphasise the merits of using MD simulations, rather than static calculations, to obtain activation barriers for ion migration in the high-symmetry forms of distorted perovskites.