It is possible to damage your car by driving fast, but most of the damage is done through rapid acceleration. Flooring the gas will essentially start a chain reaction of your engine components crashing together. This means that you can damage your pistons, connecting rods, transmission, axles, etc. by speeding up too quickly.
Maintaining a steady, high speed, however, won’t cause too much damage to your vehicle. Just try to accelerate slowly in order to reach a high speed and, if you can, brake just as slowly to avoid damaging your brakes.