Streaming high quality audio/video (AV) from home media sources to TV sets over a wireless local area network (WLAN) is a challenging problem because of the fluctuating bandwidth caused by interference. Our approach is to adjust the video bit-rate dynamically in order to improve the experienced audiovisual quality. The effectiveness of rate adaptation depends on the accurate and timely estimation of the available bandwidth. In this paper we specifically focus on robust video streaming with IEEE 802.11e medium access control (MAC) enhancements for quality-of-service (QoS). These enhancements to 802.11e increase the WLAN throughput and decrease packet latencies. However, bandwidth estimation methods used in prior work, based on packet dispersion measurements, cannot be used in this context. To address this problem, we propose a new on-line application-layer bandwidth measurement method that runs at the sender application and uses the differences of packet send times and feedback receive times. The bandwidth estimation technique is implemented in a video streaming simulation environment that also includes a delay-constrained rate adaptation algorithm at the sender. Experimental results show that streaming with bandwidth estimation and rate adaptation achieves a PSNR gain up to 3.3 dB compared to streaming without rate adaptation.