With the rise of vertical segmentation in real-world data, federated graph-level clustering has gained significant attention in recent years. However, the inherent missing attributes in graph datasets held by certain clients lead to suboptimal local parameter updates and misaligned global parameter consensus. This results in knowledge shifts during negotiation to ultimately impair overall clustering performance. This issue remains largely underexplored in the current advanced research. To bridge this gap, we propose a novel deep learning network called Federated Graph-level Clustering Network with Attribute Inference (FedAI), which utilizes high-confidence prior knowledge from each domain and multi-party collaborative optimization to achieve efficient reasoning of unknown features. Specifically, on the client, we project high-confidence graph samples into a latent space, extracting and uploading their irreversible path digest information and structure-guided inference signal. On the server, we first hierarchically identify affinity relationships by the improved graph kernel method. We then infer attributes of clients lacking attributes through a prior attribute-oriented inference signal, facilitating inter-client knowledge transfer for better clustering. Experimental results on 15 cross-dataset and cross-domain non-IID graph datasets demonstrate that FedAI consistently outperforms existing methods. Our source codes are available at https://github.com/H00001/FedAI.