We introduce FPG-NAS, a FLOPs-aware Gated Differentiable Neural Architecture Search framework for efficient 6DoF object pose estimation. Estimating 3D rotation and translation from a single image has been widely investigated yet remains computationally demanding, limiting applicability in resource-constrained scenarios. FPG-NAS addresses this by proposing a specialized differentiable NAS approach for 6DoF pose estimation, featuring a task-specific search space and a differentiable gating mechanism that enables discrete multi-candidate operator selection, thus improving architectural diversity. Additionally, a FLOPs regularization term ensures a balanced trade-off between accuracy and efficiency. The framework explores a vast search space of approximately 10\textsuperscript{92} possible architectures. Experiments on the LINEMOD and SPEED+ datasets demonstrate that FPG-NAS-derived models outperform previous methods under strict FLOPs constraints. To the best of our knowledge, FPG-NAS is the first differentiable NAS framework specifically designed for 6DoF object pose estimation.