Next-generation mobile networks (such as Fifth-Generation (5G), and Sixth-Generation (6G)) are envisioned to undergo an unprecedented transformation from connected things to connected intelligence with more stringent characteristics, i.e., low end-to-end latency, high bandwidth, reliable connectivity, etc. Such networks will significantly increase network traffic in the distribution networks, causing the need for real-time automated decision-making, such as automated network resource allocation. The network resources must be allocated dynamically based on the Quality of Service (QoS) requirements. However, the primary concern is that the distribution networks may get congested soon after allocating network resources. Thus, a QoS-aware prediction framework can be used proactively to predict the future trend of network traffic in each QoS class. In this paper, we propose a framework for predicting the heterogeneous multivariate QoS-aware network traffic to make the best use of network resources dynamically. Specifically, we use a Recurrent Neural Network (RNN) to integrate a Bidirectional Long Short-Term Memory (BLSTM) neural network. The results show that the fusion of RNN-BLSTM can predict the QoS-aware network traffic for over 13 hours with an average accuracy of 97.68%. Moreover, the proposed model is trained and tested over limited data, collected and identified through Deep Packet Inspection (DPI) over an operational network. In addition, we compared the RNN-BLSTM with other prediction algorithms (i.e., LSTM, ARIMA, SVM) in terms of precision, execution time, and energy consumption. Lastly, the proposed framework is used to assign the network resources to each QoS class based on the QoS requirements of that class and its pre-defined priority.