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Surface grading, the process of leveling an uneven area containing pre-dumped sand piles, is an important task in the construction site pipeline. This labour-intensive process is often carried out by a dozer, a key machinery tool at any construction site. Current attempts to automate surface grading assume perfect localization. However, in real-world scenarios, this assumption fails, as agents are presented with imperfect perception, which leads to degraded performance. In this work, we address the problem of autonomous grading under uncertainties. First, we implement a simulation and a scaled real-world prototype environment to enable rapid policy exploration and evaluation in this setting. Second, we formalize the problem as a partially observable markov decision process and train an agent capable of handling such uncertainties. We show, through rigorous experiments, that an agent trained under perfect localization will suffer degraded performance when presented with localization uncertainties. However, an agent trained using our method will develop a more robust policy for addressing such errors and, consequently, exhibit a better grading performance.