We explore the equation of state for nuclear matter in the quark-meson coupling model, including full Fock terms. The comparison with phenomenological constraints can be used to restrict the few additional parameters appearing in the Fock terms which are not present at the Hartree level. Because the model is based upon the in-medium modification of the quark structure of the bound hadrons, it can be readily extended to include hyperons and to calculate the equation of state of dense matter in β equilibrium. This leads naturally to a study of the properties of neutron stars, including their maximum mass, radii, and density profiles.