As the threat of Covid-19 continues and in the face of vaccine dose shortages and logistical challenges, various deployment strategies are being proposed to increase population immunity levels. How timing of delivery of the second dose affects infection burden but also prospects for the evolution of viral immune escape are critical questions. Both hinge on the strength and duration (i.e. robustness) of the immune response elicited by a single dose, compared to natural and two-dose immunity. Building on an existing immuno-epidemiological model, we find that in the short-term, focusing on one dose generally decreases infections, but longer-term outcomes depend on this relative immune robustness. We then explore three scenarios of selection, evaluating how different second dose delays might drive immune escape via a build-up of partially immune individuals. Under certain scenarios, we find that a one-dose policy may increase the potential for antigenic evolution. We highlight the critical need to test viral loads and quantify immune responses after one vaccine dose, and to ramp up vaccination efforts throughout the world.