If you have doubt about being able to handle it, I would leave once she's down and well asleep. You don't need to watch her go, and if it's comforting her that you're worried about, once she's sleeping, she won't know if you've stayed or gone. I've never seen a horse euthanized, though I have seen them die without it. I'm not trying to scare you or anything, but if the end stage with euthanasia is anything like end stage without, let your last memory be of her sleeping peacefully on the ground. SHE won't be suffering, but it can be traumatizing for US.

I'm sorry you're dealing with this, and with a fairly young horse, too. It's never easy to lose one.