Emerging network application paradigms, such as the Tactile Internet, re-emphasize the need for different Quality of Service (QoS) levels. Due to the large packet buffers in the underlying network data plane, Active Queue Management (AQM) is generally required to curtail packet latencies for flows requiring high QoS levels. At the same time, programmable data planes, such as P4, enable packet processing at line-speed, albeit with limited packet processing functionalities. However, the existing AQM mechanisms that support QoS differentiation are too complex to readily run on P4, while the existing AQM mechanisms that run on P4 do generally not support effective QoS differentiation. We address this gap by developing to the best of our knowledge the first AQM mechanism that supports effective QoS differentiation while running on P4. Specifically, we propose SP-CoDel, which combines the well-known Controlled Delay (CoDel) AQM mechanism with Static Priority (SP) scheduling for QoS differentiation. Also, we propose RED-SP-CoDel, which adds a RED AQM component to SP-CoDel so as to make the AQM with priorities essentially parameterless. As a community resource contribution, we substantially extend the existing P4Simulator to the novel fused P4-NS3 Simulator so as to enable the evaluation of packet processing mechanisms through the combined functionalities of P4 device emulation and NS3 packet simulation. Evaluations conducted with the P4 reference switch model in the P4-NS3 Simulator indicate that SP-CoDel and RED-SP-CoDel provide high QoS to high-priority data streams, i.e., significantly reduce latency and packet loss compared to CoDel, while effectively mitigating bufferbloat.