I would actually, instead of killing bugs that freak her out (particularly ones that don’t bite,) do something similar to what @snowberry suggests but on a smaller scale. Especially if your girl is already taking care of a bug and seeing it’s life too. So if/when she freaks out, if you can do so, gently and calmly catch the bug with you bare hands, if it’s something that bites/stings I always use a cup+paper, or whatever I can get it to crawl on… even though I know it won’t really hurt me. And let it free somewhere. My sister wish we’d known the bug-keeper-idea! has been scared of spiders, turned to anything that’s little and crawls, since a spider fell on her head in the shower when she was little. After her fear, she use to squish them, and I got her to find me so I could let the bug outside, and it could keep its life. Now, although it’s been slow, it’s to the point where she’ll catch them, so long as she’s got a cup and paper, and let them outside. And then, she’s saving their lives, too, letting them live out in the wild where they can find food (and if they’re a spider, eat other bugs!) They don’t bother her less, so it’s not perfect, but she appreciates their life, now, at least, and has a way of dealing with it, and is willing to get close-ish.
I think what @snowberry said would work better at lessening the fear. Mine’s just moving it.
When I was little, my dad actually introduced my sister and me to daddy longlegs spiders, and we had no fear of insects. We’d actually search for the poor daddy longlegs to let them crawl on our hands. Free pets! (Careful not to harm them, though.) Same with my mom outside in the garden, she’d explain to use how bees and ladybugs and butterflies all help the plants, and when we found ladybugs, we’d get to let them crawl on us. Pillbugs too, although we called them rollie pollies. And actually, june bugs too… and mayflies (although I’m not confident anymore that what I know as june bugs and mayflies are the true ones.) They made a game out of saving the indoor/in-water insects; life, and showed us bugs don’t want to harm us.
Mosquitos, though, we squish.
That all worked until we learned from other kids to be scared of bees and wasps, spiders, etc, and my sister had her traumatic incident. We were even told by one kid that daddy longlegs had the most potent poison in the world, just their fangs aren’t strong enough to puncture our skin… I wonder if it wasn’t things like this, little stories, or watching other kids be scared, that scared your girl? Just a guess, though, because that’s what happened with us.