Following another drone does not seem so simple as you make it sound. For one thing, you would need your own drone to be at the ready at al times, with range and speed and agility at least equivalent if not superior to whatever might appear anywhere at any time.
Better would be some sort of electronic signature acquisition and the ability to track where that drone is getting its piloting info from. But, with AI making drones more autonomous, there might not even be a signal controlling it, soon.
For military installations, something like a laser cannon seems most useful. If a drone is flying in a restricted area, shoot it down.
But, for some sort of assassin drone operating on Wall Street (or your neighborhood) that uses facial recognition to put a single bullet where it is assigned to deliver it, defense would be a lot harder. And, if drones become common for delivering packages, birthday displays and songs, etc. as well as sport and personal photography, spotting one that has malevolent purpose ahead of time would likely be impossible in the cluttered sky.
There does need to be better regulation of drones. Calling them "aircraft" and trying to protect them under the rules of "aircraft" is disingenuous, because those rules were meant for air vehicles piloted by people in them. And those pilots need to file flight plans. And, they need to respond to radio communications from air traffic controllers and even intercepting military aircraft.
One thought is that drones could be required to have identity and position indicating transponders in them, and those that do not respond to interrogation are shot down without any more "due process".