The shaking isn't an unusual response to the effort of an isometric exercise like a plank. It happens because your tired muscles are "grabbing" as they try to fail and you demand that they keep working.
It will take longer to start as you get stronger. In the meantime, keep focusing on good form, clench your abs and glutes, grit your teeth, and ... um ... enjoy. You don't need to quit the rep until you lose form (not necessarily when you start shaking).