A precise Quality-of-transmission (QoT) estimation of a Lightpath (LP) before its deployment is a key step in effective network design and resource utilization. Deep neural network-based methods have recently shown promising results for QoT estimation tasks. However, these methods contain a large number of parameters and require heavy computational resources for accurate predictions. To this end, we propose a novel Knowledge distillation (KD) based compression method to obtain a compact and more accurate model for QoT estimation. Our simulation results demonstrate that the model trained using KD significantly improves accuracy with reduced parameters and computational complexity. To the best of our knowledge, this is the first time that the knowledge distillation technique has been used to estimate the QoT of an unestablished LP.