The best place to start is to do a literature review of the tools used to measure QoL. See what tools are currently used in the literature and find one that is appropriate for your research questions.
If you are looking at Health-Related QoL in adolescents these articles might be helpful.
Frisén, A. (2007). Measuring health‐related quality of life in adolescence. Acta Paediatrica, 96(7), 963-968. https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.1651-2227.2007.00333.x?casa_token=z1lb9d-r7hQAAAAA:3T6sx2eZiPE9LuIJbdv-g6UG3WEUuU4d0INVXHZxe6LWc9PwxNd-fP0g6tST2R0axA1KsJaqhoifu7U9
Wilkins‐Shurmer, A., O'Callaghan, M., Najman, J. M., Bor, W., Williams, G. M., & Anderson, M. J. (2003). Association of bullying with adolescent health‐related quality of life. Journal of Pediatrics and Child Health, 39(6), 436-441.
Article Association of bullying with adolescent health‐related quality of life
To the best of my knowledge there is no specific toll develop till now to measure the quality of life impact on population with victim of bullying. I believe that one should measure anxiety and depression in that case instead of Qol.