We report fully quantum simulations of realistic models of boron-doped graphene-based field effect transistors, including atomistic details based on DFT calculations. We show that the self-consistent solution of the three-dimensional (3D) Poisson and Schrodinger equations with a representation in terms of a tight-binding Hamiltonian manages to accurately reproduce the DFT results for an isolated boron-doped graphene nanoribbon. Using a 3D Poisson/Schrodinger solver within the Non-Equilibrium Greens Functions (NEGF) formalism, self-consistent calculations of the gate-screened scattering potentials induced by the boron impurities have been performed, allowing the theoretical exploration of the tunability of transistor characteristics. The boron-doped graphene transistors are found to approach unipolar behavior as the boron concentration is increased, and by tuning the density of chemical dopants the electron-hole transport asymmetry can be finely adjusted. Correspondingly, the onset of a mobility gap in the device is observed. Although the computed asymmetries are not sufficient to warrant proper device operation, our results represent an initial step in the direction of improved transfer characteristics and, in particular, the developed simulation strategy is a powerful new tool for modeling doped graphene nanostructures.