Has SHE ever SHOT a .40 S&W? You said you "think" she can handle it. Like a poster above mentioned, some of the compact ones, can have a pretty good rap to them.
If she can handle the round (and an auto), then it's obviously and effective round to use. So is a proper 9mm for defense. I would settle on which is affordable and easier for her to shoot.
I'm old school. For a woman, I always recommend a nice 2-3" 38spl revolver for home
defense.
When buying a handgun for a woman, don't get lured into listning to all the gun-goobers
at the gunstore, telling you what you HAVE to get. Get what they can shoot.
My mother-n-law, HAD to have a .357 magnum. After half a cylinder, she realized she wasted $400. There was NO way she could have defended herself with that gun.
I bought it off of her, and picked up a used SP101 in .32H&R for her. She loves it
and shoots it alot. I KNOW she can defend herself with it.
My wife chose a S&W .32 long kit gun for her "drawer gun".
Whatever they can shoot, and shoot good.
I wish her the best with it.
Glad she chose to arm herself.