Kids...don't usually shrink.
On the other hand, if you and her father are both pretty tiny and she's already started to mature, her hands might not grow much more for a while.
I would say if you don't mind her growing out of them quickly, start with the size 1 narrows. Particularly if you know of someone else smaller you can dump them off on if she decides she wants what everyone else has as soon as she's put chalk or water on them and you can't return them. If you don't want to buy another pair of grips
in a month or two or whenever she grows before wearing the others out, grab the size 2 regulars. If her hands are big enough to fit into a size 2 anyways...
Measure *your* hands. If you're significantly taller, but your hands aren't much bigger, she might not be just waiting until the second you order grips to grow out of them.
And don't trust the size on a pair that doesn't have the size printed on it, if you're trying someone else's. They could have got them where I got my old pair...ordered a 2, got what I think must be a 0!