Censored quantile regressions can model a survival outcome without pre-specifying a parametric likelihood function or assuming a proportional hazard ratio. Existing censored quantile methods are mostly limited to fixed cross-sectional covariates, while in many longitudinal studies, researchers wish to investigate the associations between longitudinal covariates and a survival outcome. We propose a framework that jointly model a longitudinal covariate process, conditional quantiles of a survival outcome and their associations. This framework is an extension of a censored quantile based data augmentation algorithm (Yang, Narisetty and He, 2018), to allow for a longitudinal covariate process in presence of different forms of censoring schemes. We apply the proposed method to the LEGACY Girls cohort Study to understand the influence of individual genetic profiles on the pubertal development (i.e., the onset of breast development) while adjusting for BMI growth trajectories. The results are compared favorably to the likelihood based joint modeling of survival and longitudinal data. In the meantime, we found new insight on the puberty growth of girls with breast cancer family history.