We present a transportable ultra-stable clock laser system based on a Fabry-Perot cavity with crystalline Al0.92Ga0.08As/GaAs mirror coatings, fused silica (FS) mirror substrates, and a 20 cm-long ultra-low expansion (ULE) glass spacer with a predicted thermal noise floor of mod σy = 7 × 10-17 in modified Allan deviation at one second averaging time. The cavity has a cylindrical shape and is mounted at 10 points. Its measured sensitivity of the fractional frequency to acceleration for the three Cartesian directions are 2(1) × 10-12 /(ms-2), 3(3) × 10-12 /(ms-2), and 3(1) × 10-12 /(ms-2), which belong to the lowest acceleration sensitivities published for transportable systems. The laser system's instability reaches down to mod σy = 1.6 × 10-16.