Multi-label intent detection aims to assign multiple labels to utterances and attracts increasing attention as a practical task in task-oriented dialogue systems. As dialogue domains change rapidly and new intents emerge fast, the lack of annotated data motivates multi-label few-shot intent detection. However, previous studies are confused by the identical representation of the utterance with multiple labels and overlook the intrinsic intra-class and inter-class interactions. To address these two limitations, we propose a novel dual class knowledge propagation network in this paper. In order to learn well-separated representations for utterances with multiple intents, we first introduce a label-semantic augmentation module incorporating class name information. For better consideration of the inherent intra-class and inter-class relations, an instance-level and a class-level graph neural network are constructed, which not only propagate label information but also propagate feature structure. And we use a simple yet effective method to predict the intent count of each utterance. Extensive experimental results on two multi-label intent datasets have demonstrated that our proposed method outperforms strong baselines by a large margin.