Reshetikhin-Turaev a.k.a. Chern-Simons TQFT is a functor that associates vector spaces to two-dimensional genus g surfaces and provides projective representations of the mapping class groups. There is growing evidence that there exists a Macdonald q, t-deformation – refinement -of these TQFT representations. We will substantiate this claim by explicitly constructing the refined TQFT representation of the genus 2 mapping class group, in the case of rank one TQFT. This is a direct generalization of the original genus 1 construction of arXiv:1105.5117, opening a question if it extends to any genus. Our construction is built upon a novel q, t-deformation of the square of q-6j symbol of Uq(sl2), which we define using the Macdonald version of Fourier duality.