We show that the (2 + 1)-dimensional [Formula: see text]-Dirac oscillator is equivalent, to the first-order of the deformation parameter, to a couple of simultaneous Jaynes–Cummings (JC) and Anti-Jaynes–Cummings (AJC) models with opposite chiralities, where the former is entirely due to the deformation. The energy eigenvalues and the corresponding eigenfunctions of system are obtained in a simple manner from the solutions of the non-deformed Dirac oscillator by mapping the complete system to a single AJC model through a similarity transformation. The pseudo-supersymmetry and other interesting features of the system are also discussed.