Sammie sees herself for the first time!

This morning Sammie, who is all of five months, caught a glimpse of herself in my glass fireplace doors. At first, I was reading nearby, I couldn't figure out why she was sending forth a tsunami of barking and growling. Then I noticed that she was fixated on the hearth. I stood up and looked. Sure enough, her exact image was looking back at her. Of course she thought it was another little terrier, and she was not going to give her an inch! The caterwauling went on for a few minutes, and then S. began to dance around a bit and inch up toward the fireplace. Gradually, she got right on top of it and pressed her nose to the glass. The crying continued until she backed up again..... Anybody have an idea of how to handle this? I'm thinking of hanging a blanket over the glass when we're in the room. Otherwise, if Sanmmie keeps on seeing rival pups, she will have to be banished, or she'll never stop tilting at windmills, or imaginary Shih Tzus!