The wave-packet convergent close-coupling (WP-CCC) approach is applied to calculate the energy spectrum of electrons ejected in p+H2 collisions as a function of the scattering angle of the projectile. The calculations are performed for projectile energies of 75, 100, and 200 keV. At these incident energies there are many competing reaction channels that play an essential role in the collision dynamics. The target is modeled as an orientationally averaged effective one-electron system. The results are compared with available perturbative calculations and experimental data. Good agreement between the WP-CCC results and experimental data is found for small emission energies, especially when the projectile is scattered at small angles. However, when the electron is emitted with a speed comparable to or greater than the projectile speed, we find that our method predicts smaller cross sections near zero scattering angles and a slower fall off than the experimental data. This is in agreement with other calculations. Furthermore, the structure observed in the experimental data at large scattering angles is not supported by our results. Interestingly, we find very good agreement with the continuum-distorted-wave eikonal-initial-state molecular-orbital calculations that use a two-effective center approximation, though our method describes the target as an effective one-electron spherically symmetric system. This suggests that in these models two-center interference effects may have a small effect on this particular cross section. Furthermore, we find that the experimentally observed decrease in average scattering angle in proton collisions with H2 near the electron-projectile matching speed is not reproduced by our results. We also present the doubly differential cross section for ionization as a function of the scattering angle of the projectile at select emission angles.