The Empty should not be placed where you say you placed it.
It must be on the Line passing through the camera and perpendicular to the Mirror plane (even if bumped) and at a distance from the plane equal to the distance of the camera from that same plane, but on the other side. Axis Y pointing to the plane.
This should solve.
If I may I would like to criticize the moon:
1st - Its texture is wrong. You can see on moon’s top those lines stretching? You solve this by using ‘Sphere’ Mapping for the texture.
2nd - Moon looks oval, not spherical
3rd - Moon is too dull gray, and, even worse, its reflection in water is brighter than moon itself :o