Not to be nasty or preachy, simply to offer up some other points to consider. Do you know how long the overall treatment is expected to take? Both my DDs started their ortho treatment on the early end of the spectrum amongst their peers, which they both kind of disliked initially, but both came to appreciate as they moved into HS & more of their peers began treatment while they were already done.
Generally orthos have an optimal time they'd like to begin certain phases of treatment depending on stage of development. Waiting longer, even a few months may mean a progression in development requiring more or longer treatment. Both of my girls went beyond initial treatment timeline estimates despite following the ortho's instructions. Many of their friends have as well. Several of my older DD's friends were very upset at having braces in senior photos -- thank goodness for Photoshop, and events like prom. A few of the kids had resisted getting braces & parents went along until their kid was ready. I know of at least 3 who wound up w/ much more involved treatment than expected because they hadn't started when they were evaluated -- granted these are cases where they were evaluated to begin 7th to 9th grade & didn't start until 10th & 11th grades, not a shorter interval like you were contemplating.