Prosumers are active participants in future energy systems who produce and consume energy. However, the emerging role of prosumers brings challenges of tracing carbon emissions behaviours and formulating pricing scheme targeting on individual prosumption behaviours. This paper proposes a novel blockchain-based peer-to-peer trading framework to trade energy and carbon allowance. The bidding/selling prices of prosumers can directly incentivise the reshaping of prosumption behaviours to achieve regional energy balance and carbon emissions mitigation. A decentralised low carbon incentive mechanism is formulated targeting on specific prosumption behaviours. Case studies using the modified IEEE 37-bus test feeder show that the proposed trading framework can export 0.99 kWh of daily energy and save 1465.90 g daily carbon emissions, outperforming the existing centralised trading and aggregator-based trading.