In this paper, a reinforcement-learning-based scheduling framework is proposed and implemented to optimize the application-layer quality-of-service (QoS) of a practical wireless local area network (WLAN) suffering from unknown interference. Particularly, application-layer tasks of file delivery and delay-sensitive communication, e.g., screen projection, in a WLAN with enhanced distributed channel access (EDCA) mechanism, are jointly scheduled by adjusting the contention window sizes and application-layer throughput limitation, such that their QoS, including the throughput of file delivery and the round trip time of the delay-sensitive communication, can be optimized. Due to the unknown interference and vendor-dependent implementation of the network interface card, the relation between the scheduling policy and the system QoS is unknown. Hence, a reinforcement learning method is proposed, in which a novel Q-network is trained to map from the historical scheduling parameters and QoS observations to the current scheduling action. It is demonstrated on a testbed that the proposed framework can achieve a significantly better QoS than the conventional EDCA mechanism.