I feel like you could probably hear it and shoot it down yourself before it would have any decent chance of hitting you. It would probably be much more effective to have the drone fly as high as possible and the gun positioned to fire straight down.
It is public and (relatively) common knowledge that an Abrams tank can fire accurately at speed over rough terrain by postponing the firing of a shell by just a fraction of a second until the gyroscopes and computers determine that tank is “floating” at the apex of a bump.
That tech has existed since the 1980’s.
The implementation shown in this gif may be noncredible, but the concept most certainly belongs in the other place.
RIGS on the original psvr used this method for aiming the guns on your mech. Obviously aiming in a game vs an actual fpv drone is different, but it was remarkably intuitive once you got over the looking one way and moving the other nausea.