In low-carbon environments, asymmetric carbon information causes the enterprises in a supply chain to face the risk of misstatements about carbon emissions. Such misstatements could affect the decisions about carbon emission transfers in the supply chain. To optimize carbon emission transfers among supply chain enterprises, this study formulates a supplier-led Stackelberg game model incorporating the government’s initial carbon emission allowances and fines. The study also examines the mechanism of the behaviors of enterprises in low-carbon supply chains, the proportions of initial quotas, the impact of government fines on carbon transfers, and the influence of the supply chain and carbon emission transfers on related supply chain decisions and profits. The main findings are as follows. First, the proportion of the government’s initial quota has a positive effect on the carbon emission transfer quantity of the supplier, while government fines and misstatement factors have a negative effect. Second, the carbon emissions of the unit product of the supplier decrease as the under-reporting factor and carbon emission transfer quantity of the supplier increase. The under-reporting factor has a stronger effect on the carbon emissions of the unit product. Third, in a carbon-free market, carbon emission transfers negatively affect the disclosed profits of the supply chain, whereas in a perfect carbon market, the carbon trading price has a certain endogenous regulation mechanism for the suppliers’ operational decisions. Fourth, the supplier’s wholesale price order quantity is negatively correlated with the supplier’s carbon emission transfer quantity, but positively correlated with the initial carbon quota ratio.