With the standardization of SVC, the scalable extension of H.264/AVC, layered peer-to-peer streaming has attracted more and more attention as it offers adaptability to network fluctuations and heterogeneous end users. Although overlay construction is important for system performance, not much effort has been spent on unstructured overlay construction for layered peer-to-peer streaming. Related work concentrates on layered streaming algorithms, and assumes that a list of peers for data exchange, called neighbors, is provided by traditional membership management protocols, e.g., SCAMP. Our previous studies have demonstrated that a random overlay is not good enough for layered peer-to-peer streaming. In this paper, we propose a new membership management protocol, based on peer sampling services. The protocol is quality-aware as it constructs the overlay so that (1) high capacity peers will be located at good positions in the overlay, e.g., close to the server, and (2) peers having similar capacity are likely to connect to each other. Both features are necessary to maximize bandwidth utilization of peers and to mitigate layer bottlenecks. With implementation of the protocol in PeerSim, we evaluate important graph properties of the overlay, constructed by the proposed protocol, to understand how it evolves during the streaming session with peer churn. Evaluation results show that the overlay is (1) scalable: it is stable with different sizes, from hundreds up to 10000 peers; and (2) robust: the good features are maintained or recovered fast under a high peer churn rate, and it only becomes disconnected when more than 86% of the peers are removed from the network.