International schools do have a very different student body than an average school, and indeed if the school draws heavily from highly educated parents, a greater percentage of the school will be gifted. Additionally, if you're in a location with limited opportunities for spousal employment, highly educated spouses unable to work will often use significant resources (tutoring/extra homework/etc.) to ensure that their children succeed at many different things, including school. This is most certainly the case in our location, and our school (private international with a UK curriculum) is very high achieving with very pushy parents.
Our experience at such a school, with lower elementary students, is that the teaching staff is incredible. They meet kids where they are and are particularly sensitive to new kids. The entire transition for your children is overwhelming, and the school knows that and will help them to succeed. Hopefully, your new school is able to attract and support a stellar teaching staff.
I've found that because my kids work at such a high level, they haven't had to do the drill work that other kids have done, but they are also not grade skipped. If your girls have been grade skipped, they will be in for significant challenge if your school is similar to ours, as the general level is already at least half a grade to a full grade higher than a good school back home. For example, my K'er did second grade math in class with other advanced/gifted kids. It was still easy for him, but the school has enough K kids working that far ahead to offer than in class. Any child actually working on K level curriculum was behind.
First off, don't stress too much about the school until you're settled. You may find the lifestyle in your new location to be significantly different from home, and you may adjust and find the situation "normal" quickly enough. Give yourself and your kids time to adjust to all of the newness, and school will sort itself out in time.
