In the early Universe, the cooling mechanisms of the gas significantly rely on the HD abundance and excitation conditions. A proper modeling of its formation and destruction paths as well as its excitation by both radiative and collisional processes is then required to accurately describe the cooling mechanisms of the pristine gas. In such media, ion–molecule reactions are dominant. Their theoretical study is challenging and state-of-the-art quantum time-independent methods are computationally limited to collisions involving light molecules. Here, we report a state-to-state scattering study of the HD–H⁺ collisional system using two different methods: an exact quantum time-independent approach and a recently developed fast and efficient statistical method. Reactive and inelastic rate coefficients were obtained for temperatures up to 300 K. The statistical method is able to reproduce exact calculations with an accuracy reaching the astrophysical needs while drastically reducing the computational resources requirements. Such results suggest that this new statistical method should be considered to provide the astrophysical community collisional data for which quantum calculations are impossible.