I would say it's nowhere near as far ahead as Grade 3 (I've been a piano teacher for 20 years). My pupils are about ready to do Prep test once they've finished book 2, so I'd say that's more or less where your daughter is. By the end of book 3 you are probably touching Grade 1 standard. She is probably just about ready to make a start on some scales and arpeggios now, so you could mention it to the teacher if she is keen.
People really underestimate just how hard Grade 1 is on the piano. It sounds so basic, too! You need to be able to read at least an octave and a half of notes in both treble and bass clef, be able to play confidently hands together where the left hand does more than just add a few accompanying chords and have a good secure sense of rhythm, dynamics and articulation to do well at Grade 1.
seeline I do wonder if your son's teacher allowed him to work on Grade 3 too early. This can make the practice too daunting and the scales next to impossible, leading to pupils becoming discouraged and giving up.
OP, I'm not saying this to discourage you, by the way! It's just that parents can sometimes think their child is doing less well than they actually are when it takes a little while to achieve Grade 1. And yes, most of my pupils learn from a variety of sources as I find it makes better sight readers and more well-rounded musicians. But that doesn't mean the teacher is necessarily wrong if the method is suiting her. :)