I don't think this story would alienate her from the MAGA base. Conservatives love the aesthetics of farm life/hunting, doing the dirty work, etc. We're talking about people who defended "grab her by the pussy".
Even Republicans have dogs and love them. I think on balance this will hurt her, even from her base. People who like their dogs (if they hear about it) will be disgusted.
But you see, only trump's opinion matters, and trump hates dogs. If he picks her, magats will fall in line and come up with rationalizations that what she did was good.
Not saying it's right, but most people feel more attachment to their dogs than to strangers (immigrants, queers, liberals etc). So while there will definitely be maga people who still support her, what I'm saying is on average, more people who might otherwise be supporters will be disturbed.
I think you're right that they'd be disturbed. But I think their cognitive dissonance will overcome that and they'll rationalize it in whatever way they need to to see it as acceptable, because in their eyes trump never makes a mistake or does anything wrong.
THIS. They will go crazy(ier) from the cognitive dissonance but they'll probably champion donnie/Kristi kind of thinking, calling dog owners "woke" and SJW, etc...
Not only that, but she comes off like a complete dumbass when it comes to handling guns. Even idtiot gun-fondlers probably noticed that, but might have to deal with the cognitive dissonance later...