I'm a 7th grade counselor at a public school. I often transition kids in from the local private schools. Don't worry, kids have a lot more space to breathe in public school. They can kind of get lost in the crowd, and that sounds like just what your daughter needs. There are a lot more people to choose from to be friends with in a public school, and she will find her own quirky companions. All you need to get through middle school are a couple good friends you can hang with at lunch, between classes, and after school. No need to be the most popular girl in school to be happy.
You won't be able to control any teasing or comments she will get in middle school, but you can teach her to be resilient, you can build her self-confidence outside of school, and give her all the right tools and comebacks to handle any little jabs that come her way.
Real bullying in school is more rare than you think- with girls it usually happens among girls that already know each other, run in the same circle, have past history from elementary school. If your daughter is getting a fresh start that's perfect, providing she finds a few nice girls to link up with, she'll be all good.
What would the IEP be providing, how does she qualify? The school counselor in me has to ask. I cannot guess how she would qualify for an IEP but also qualify to do well in the Advanced classes. (FYI, AP stands for Advanced Placement, at least where I live that program doesn't kick in until Junior year of High School, meaning they can take AP classes- which are college level courses taught at High School). If she is qualifying for an IEP due to her "mild physical handicaps" I am really curious what those are, because maybe they are not so mild if they require IEP services despite the fact she is intellectually capable enough for advanced classes.
ETA#1 No you don't have to have a MAJOR disability to be on an IEP. However, if all you require to be successful in the Gen Ed classroom is a few accommodations in testing and homework assignments, that is what a 504 plan is for. The IEP is for kids who require services OUTSIDE the scope of general education, not just a few tweaks here and there. IEP's are usually providing heavy accommodations in a Gen Ed class, or actually providing a resource class in it's place or an additional one to support it. This is why IEP's and Advanced classes do not mix. A 504 student might be able to be successful in Advanced classes with a few accommodations, but an IEP student is usually accommodated enough just to get through Gen Ed.
ETA#2 Felinestroller is right on target with Yearbook- great class for a new shy student to connect to the school and peers in a natural way. It's also a perfect class for an organized high achiever to meet other organized high achievers, who are at least somewhat outgoing.