Pingry and Lawrenceville are a fair distance apart - are you in southern or northern NJ? Is Lawrenceville still a boarding school (and I guess it must have started admitting girls, because it was all boys when I was growing up)?
I would check into the boarding school thing very carefully. There are many good schools in NJ (and depending upon your location, might have access to private schools in PA or NY). Even the great private schools in my area (SE PA) are NOT challenging in elementary school, perhaps not in middle school either. In HS, I think you have more options. Or are you just looking for a peer group and not expecting instruction at her level?
I know kids in this area who had 2100+ on their SAT in 7th grade, made USAMO prior to HS, etc. A couple did skip a grade, but clearly skipping one grade would not meet their academic needs. I am not certain that attending a different school would have served their academic needs any better. However, they did have a handful of peers in the school, as well as similar kids at nearby schools. I doubt you need to pay for boarding school to find a peer group.
I see that Pingry has about 130-140 kids per graduating class. Seems that they have had about 10 NMSF each year. That is good, but there are public schools with plenty of NMSF in NJ as well. I know there are public schools near me that have similar rates of NMSF as Pingry (percentage-wise, not total). There are public schools out there that have really bright kids. Might need to move, and I don't know if that is an option.
