
I think, with careful management, this will in all likely hood, go away.
4 months is very very young, certainly all my dogs at a young age have been curious about their reflections!
Taking Rocky for a walk along a high street when i just got him was an absolute nightmare, cos he was staring and barking at his reflection at every shop window!
Now he just accepts that they are there, and ignores it.
However, i say careful management, as it is entirely possible that your dog could find the way you react to her behaviour in some way rewarding.
If you are doing ANYTHING that might encourage her to do it more, stop! This could even be going to her, or shouting at her to shut up, if that gets her some attention, then she will remember, and do it again!
good luck,
Em