Motivated by the goal of realizing topological phases in thin films and heterostructures of correlated oxides, we propose here a quantum anomalous Hall insulator (QAHI) in ultrathin films of double perovskites based on mixed 3d-5d or 3d-4d transition metal ions, grown along [111] direction. Considering the specific case of ultrathin Ba2FeReO6, we present a theoretical analysis of an effective Hamiltonian derived from first-principles. We establish that a strong spin-orbit coupling at Re site, t2g symmetry of the low-energy d-bands, polarity of its [111] orientation of perovskite structure, and mixed 3d-5d chemistry results in room temperature magnetism with a robust QAHI state of Chern number C = 1 and a large band-gap. We uncover and highlight a non-relativistic orbital Rashba-type effect in addition to the spin-orbit coupling, that governs this QAHI state. Our prediction of a large topological band-gap of ∼ 100 meV in electronic structure, and a magnetic transition temperature Tc ∼ 300K estimated by Monte Carlo simulations, is expected to stimulate experimental efforts at synthesis of such films and enable possible practical applications of its dissipationless edge currents.