So, I decided the most practical thing to do is mount the mirror on the wardrobe's door. I will mount it inside the door which is wood.
While checking out the warddroben's door, the frick'ing door fell off and hit the floor! Wow, if I had the mirror installed, would have broken it.
Turns out, the hinge on the door has a latch. Pull the latch, and the door comes off the wardrobe without warning. It is too easy to accidentally snag on it.