Welcome to the forum!
She isn't pushing, once they start pushing they have a kid out within a half hour. If they don't and no one intervenes the doe and kid will die. I would guess she is grunting from the kids squishing her lungs (common at the end of pregnancy), and possibly starting to prolapse which can be mistaken for a kid coming out. When pushing, the does stomach tightens HARD, she pushes out her legs, and will sometimes lift her lip with each push or scream. I would guess the rapid breathing is more like a one after another grunt or umph sound? That happens when the lungs are squashed by the kid at the end of the does pregnancy.
Here is an article with a video included on how to tell when your goat is going to kid, I would highly recommend it! What to Expect When Your Nigerian Dwarf is Giving Birth (Kidding/Freshening) and When to Worry