Depression detection from speech signals has emerged as a promising non-invasive screening method, but its development is hindered by limited labeled data. While data augmentation is a common strategy to mitigate this challenge, most previous studies rely on simple sample/feature transformations or generic models that distort feature distribution or fail to capture the speaker-specific vocal characteristics required for depression detection. Therefore, in this paper, we proposed a unimodal data-augmented Mamba for speech-based depression detection, termed UniDaugMamba. First, we proposed a dual-path Mamba-based architecture that can efficiently process unimodal complementary features. Second, we proposed a voice data augmentation framework based on voice conversion and a large language model, which enabled high-quality synthetic speech generation tailored for depression detection. We conducted extensive experiments on the DAIC-WOZ dataset to investigate the optimal data augmentation strategy in terms of usage manner and proportion of synthetic data. The experiment results showed the proposed data augmentation methods outperformed the traditional method (such as adding noise or spectral masking). Moreover, a minimalist augmentation strategy (a 0.1x ratio) with simple data mixing is more effective than both massive data volumes and complex training paradigms. Finally, the proposed UniDaugMamba achieved highly competitive performances compared to the state-of-the-art methods for unimodal depression detection.