I don't think it will hurt her that much, but that is a video clip that can be played over and over.
You just don't give the opposition something like that. Time will tell if it fades away, like BenGassy, or becomes a general meme. It will certainly become a whacko right-wing meme. The only question is if it will have any traction in general, which I doubt.
Especially if trump or the GOP starts with women/dog jokes. These things are also fraught with danger for the mockers.
Also speaks volumes about demagogues, that this is the level they dig up and think is "significant".
It's sad really.