In this article we propose a general Bayesian estimation framework for the Birnbaum-Saunders Quantile Regression (BSQ) model which is used to analyze asymmetric and heterogeneous economic data. In this work, the novel aspect is the joint incorporation of several existing surrogate structures (with different degrees of approximation) and decision-theoretic loss functions (with direct impact on estimation performance trade-offs) under a common BSQ framework conducive to systematic testing of their effect on quantile estimation performance. We consider two previous prior specifications which are Jeffreys prior and weakly informative priors together with three loss functions quadratic, LINEX and the proposed quadratic-logarithmic loss function. Iraqi economic data analysis demonstrates significant disparities in independent variable impacts across quantiles, confirming heterogeneous distribution. The results show further that Jeffreys prior yields more consistent estimates in most quantiles, whereas weakly informative priors give better coverage under the tail. Also, this highlights the importance of choosing a loss function and motivates asymmetric and hybrid loss functions for improved accuracy, especially in extreme quantiles. This contribution expands upon previous works by introducing a new general comparative framework that overextends the potential of Bayesian BSQ modelling, providing robustness and flexibility in such context with significant practical function resulting estimation improves in economic real-world applications.