Fabrication techniques at the nanometer scale offer potential opportunities to access single-dopant features in nanoscale transistors. Here, we report full-band quantum transport simulations with hole-phonon interactions through a device consisting of two gates-all-around in series and a p-type Si nanowire channel with a single dopant within each gated region. For this purpose, we have developed and implemented a mode-space-based full-band quantum transport simulator with phonon scattering using the six-band k · p method. Based on the non-equilibrium Green's function formalism and self-consistent Born's approximation, an expression for the hole-phonon interaction self-energy within the mode-space representation is introduced.