Differentially-Private SGD (DP-SGD) and its adaptive variant DP-Adam are powerful techniques to protect user privacy when using sensitive data to train neural networks. During training, converting model weights and activations into low-precision formats, i.e., quantization, can drastically reduce training times, energy consumption, and cost, and is thus a widely used technique. In this work, we demonstrate for the first time that quantization causes significantly higher accuracy degradation in DP training compared to regular SGD. We observe that this is caused by noise injection, which amplifies quantization variance, leading to disproportionately large accuracy degradation. To address this challenge, we present DPQuant, a dynamic quantization framework that adaptively selects a changing subset of layers to quantize at each epoch. Our method combines two key ideas that effectively reduce quantization variance: (i) probabilistic sampling that rotates which layers are quantized every epoch, and (ii) loss-aware layer prioritization, which uses a differentially private loss sensitivity estimator to identify layers that can be quantized with minimal impact on model quality. This estimator consumes a negligible fraction of the overall privacy budget, preserving DP guarantees. Empirical evaluations on ResNet18, ResNet50, and DenseNet121 across a range of datasets demonstrate that DPQuant consistently outperforms static quantization baselines, achieving near Pareto-optimal accuracy-compute trade-offs and up to $2.21\times$ theoretical throughput improvements on low-precision hardware, with less than 2% drop in validation accuracy. We further show that our framework extends to DP-Adam with similar gains.