We present a first-principles investigation of the structural, electronic, and magnetic properties of the pristine and Fe-doped alpha-MnO2 using density-functional theory with extended Hubbard functionals. The onsite U and intersite V Hubbard parameters are determined from first-principles and self-consistently using density-functional perturbation theory in the basis of Lowdin-orthogonalized atomic orbitals. For the pristine alpha-MnO2 we find that the so-called C2-AFM spin configuration is the most energetically favorable, in agreement with the experimentally observed antiferromagnetic ground state. For the Fe-doped alpha-MnO2 two types of doping are considered: Fe insertion in the 2 x 2 tunnels and partial substitution of Fe for Mn. We find that the interstitial doping preserves the C2 AFM spin configuration of the host lattice only when both onsite U and intersite V Hubbard corrections are included, while for the substitutional doping the onsite Hubbard U correction alone is able to preserve the C2-AFM spin configuration of the host lattice. The oxidation state of Fe is found to be +2 and +4 in the case of the interstitial and substitutional doping, respectively, while the oxidation state of Mn is +4 in both cases. This work paves the way for accurate studies of other MnO2 polymorphs and complex transition-metal compounds when the localization of 3d electrons occurs in the presence of strong covalent interactions with ligands.