Although Alzheimer's disease detection via MRIs has advanced significantly thanks to contemporary deep learning models, challenges such as class imbalance, protocol variations, and limited dataset diversity often hinder their generalization capacity. To address this issue, this article focuses on the single domain generalization setting, where given the data of one domain, a model is designed and developed with maximal performance w.r.t. an unseen domain of distinct distribution. Since brain morphology is known to play a crucial role in Alzheimer's diagnosis, we propose the use of learnable pseudo-morphological modules aimed at producing shape-aware, anatomically meaningful class-specific augmentations in combination with a supervised contrastive learning module to extract robust class-specific representations. Experiments conducted across three datasets show improved performance and generalization capacity, especially under class imbalance and imaging protocol variations. The source code will be made available upon acceptance at https://github.com/zobia111/SDG-Alzheimer.