Direct Preference Optimisation (DPO) is widely used for safety alignment in large language models. However, prior work shows it is brittle and exhibits poor out-of-distribution (OOD) generalisation. In this paper, we investigate whether Curriculum Learning can improve the robustness of DPO-based safety alignment. We propose Staged-Competence, a curriculum-based framework that organises preference data by difficulty, employs competence-based sampling, and progressively updates the reference model during training. Averaged across three model families, Staged-Competence reduces OOD harmful response rates by 16% and jailbreak attack success rates by 20%, while preserving general capabilities with near-zero over-refusal. We further show that Staged-Competence (1) matches baseline safety with only 75% of the training data and (2) yields better separation between safe and unsafe responses. Staged-Competence is agnostic to the policy optimisation loss and can extend to other DPO variants and alignment domains. Our code and data are available at https://github.com/Sandeep5500/curriculum-learning-for-safety.