Neural speech codecs are key to speech transmission and storage, but most use uniform quantization across frames, allocating the same bitrate regardless of content and wasting bits. We propose VoCodec, a low-bitrate streamable neural speech codec with voicing-driven quantization that assigns higher bitrate to voiced frames and lower bitrate to unvoiced frames according to perceptual sensitivity. VoCodec embeds a voicing detector in a fully causal encoder-quantizer-decoder neural coding framework, using residual scalar-vector quantization for voiced frames and simple scalar quantization for unvoiced ones. Experiments show that on the LibriTTS dataset at a 16 kHz sampling rate, VoCodec outperforms baseline neural speech codecs even at a bitrate as low as 1.1 kbps. Our further experiments also confirm that introducing voicing-driven quantization can effectively reduce the bitrate by approximately 27% compared with uniform quantization strategy.