Knowledge Distillation (KD) is one of the approaches to reduce the size of Large Language Models (LLMs). A LLM with smaller number of model parameters (student) is trained to mimic the performance of a LLM of a larger size (teacher model) on a specific task. For domain-specific tasks, it is not clear if teacher or student model, or both, must be considered for domain adaptation. In this work, we study this problem from perspective of telecom domain Question-Answering (QA) task. We systematically experiment with Supervised Fine-tuning (SFT) of teacher only, SFT of student only and SFT of both prior to KD. We design experiments to study the impact of vocabulary (same and different) and KD algorithms (vanilla KD and Dual Space KD, DSKD) on the distilled model. Multi-faceted evaluation of the distillation using 14 different metrics (N-gram, embedding and LLM-based metrics) is considered. Experimental results show that SFT of teacher improves performance of distilled model when both models have same vocabulary, irrespective of algorithm and metrics. Overall, SFT of both teacher and student results in better performance across all metrics, although the statistical significance of the same depends on the vocabulary of the teacher models.