A plane mirror image approaches the object at the same rate the object approaches the mirror. So the speed of approach is twice the speed at which the object approaches the mirror. If the object approaches the mirror at a speed greater than half the speed of light (c), does that mean that the speed of approach between object and image will exceed the speed of light?
The real question to ask is, if this were true, could information be transmitted FTL? An easy way to answer these questions is usually by saying the light source is a photon gun that shoots a continuous stream of photons, and drawing out the path of the stream.
A similar question that can be answered the same way is the one where you have two "photon guns" oriented such that their streams are crossing, and then quickly (at a speed ~.9c) turning them so their streams are parallel. You might naively think that their intersection point flies away FTL.