Yes. You definitely should.

My DS had similar scores to your DD, and I've had similar reservations about submitting a DYS application. To us, he presents as gifted but not HG(+), so it's really hard for us to know what exactly about him is "2 or more grade levels above."

I think we're going to go through with it. I just need to get up the nerve to ask his teacher (at a gifted school) to fill out the nominator form.