The problem studied is one of quickest detection of an anomaly that emerges in a sensor network, and which may move across the network after it emerges. Each sensor in the network is characterized by a non-anomalous and an anomalous data-generating distribution, and these distributions could be different across the sensors. Initially, the observations at all the sensors are generated according to their corresponding non-anomalous distribution. After some unknown but deterministic time instant, a dynamic anomaly emerges in the network, affecting a different sensor as time progresses. The observations generated by the affected sensor follow the corresponding anomalous distribution. The goal is to detect the onset of the dynamic anomaly as quickly as possible, subject to constraints on the frequency of false alarms. This detection problem is posed in a quickest change detection framework where candidate stopping procedures are evaluated according to a delay metric that considers the worst trajectory of the dynamic anomaly. A detection rule is proposed and established to be asymptotically optimal as the mean time to false alarm goes to infinity. Finally, numerical results are provided to validate our theoretical analysis.