We present an optomechanical method for locally measuring the rheological properties of complex fluids in the ultra-high frequency range (UHF). A mechanical disk of microscale volume is used as a small-amplitude oscillating probe that monitors the fluid at rest in thermal equilibrium, while the oscillation is detected by optomechanical transduction within a sub-millisecond measurement time, thanks to an optimized signal collection. An original analytical model for fluid-structure interactions is used to extract from these measurements the rheological properties of liquids over the frequency range 100 MHz - 1 GHz. This new micro-rheology method is calibrated by measurements on liquid water, in which we observe pronounced compressibility effects above 500 MHz, but which we show remains Newtonian all over the explored range. In contrast, measurements reveal that liquid 1-decanol exhibits a non-Newtonian behavior, with a frequency-dependent viscosity associated to several relaxation frequencies in the UHF. Our data agree well with an extended Maxwell model for the viscosity of this alcohol, involving two relaxation times of 797 and 151 picoseconds, which are respectively analyzed as supramolecular and intramolecular relaxation processes. A shear elastic response of the liquid appears at the highest frequencies, compatible with the entropic elasticity of molecules as they attempt to uncurl, and whose value enables estimating the volume of a single molecule of liquid. UHF optomechanical micro-rheology demonstrates here a direct mechanical access to the fast molecular dynamics at play in a liquid, in a quantitative manner and in a short time.