When I use a stimpak on her, she dies. Is this a game glitch?

Did she get stung by a cazador, scorpion or nightstalker?

Yeah, I figured it out after a little more reading. I also can't figure out how to unpoison my companions.

The Wiki indicates two methods. the first is to turn hardcoe off, let the companion heal himself (in casual mode they are Essential and will not die from the poison—although they may go unconscious.)

Now I can't verify this because I do not play on hardcoe. I cannot toggle it ON, mid-game. Therefore I cannot confirm that you can toggle it OFF and then back ON. If you can, this should work. You will, however, lose the hardcoe Achievement (big Whoop!)

The second method is to dismiss the Companion. Again, I can't confirm this. I am dubious, because a Companion is only Essential while being a Companion.

YMMV

Either give them the Anti Venom through the Inventory System, or just take one yourself. If the companion has them, they will take them as needed. However it seems that if I take the Anti Venom, then it takes care of the companion too.

I've given them one, and they don't take it. But I have not tried giving them one and then taking one myself, I always take it first. I'll try that.

They are supposed to take it but I have noticed that they typically do not. Companions will auto clear the poison after a while, so it may be that it was only after I got fed up with them passing out that I took the Anti Venom the same time they cleared themselves. However I do remember taking an antivenom right after Boone got stung one time and he stopped moaning. So, I will have to go hunt some cazadores and test this to see if it is consistent. If it is, then it makes it easier as typically everyone gets poisoned, not just one, at least for me.