Increasing privacy and security concerns in intelligence-native 6G networks require quantum key distribution-secured semantic information communication (QKD-SIC). In QKD-SIC systems, edge devices connected via quantum channels can efficiently encrypt semantic information from the semantic source, and securely transmit the encrypted semantic information to the semantic destination. In this paper, we consider an efficient resource (i.e., QKD and KM wavelengths) sharing problem to support QKD-SIC systems under the uncertainty of semantic information generated by edge devices. In such a system, QKD service providers offer QKD services with different subscription options to the edge devices. As such, to reduce the cost for the edge device users, we propose a QKD resource management framework for the edge devices communicating semantic information. The framework is based on a two-stage stochastic optimization model to achieve optimal QKD deployment. Moreover, to reduce the deployment cost of QKD service providers, QKD resources in the proposed framework can be utilized based on efficient QKD-SIC resource management, including semantic information transmission among edge devices, secret-key provisioning, and cooperation formation among QKD service providers. In detail, the formulated two-stage stochastic optimization model can achieve the optimal QKD-SIC resource deployment while meeting the secret-key requirements for semantic information transmission of edge devices. Moreover, to share the cost of the QKD resource pool among cooperative QKD service providers forming a coalition in a fair and interpretable manner, the proposed framework leverages the concept of Shapley value from cooperative game theory as a solution. Experimental results demonstrate that the proposed framework can reduce the deployment cost by about 40% compared with existing non-cooperative baselines.