Gosh, this is really a complex decision (that's probably the reason we're all getting into it!).
I do not think that a thirteen year old should have to shoulder all the responsibility - after all it involves a move across the globe, into a very unfamiliar environment.
I would approach the process two ways: going forward and going backward.
Going forward, you have decided it is best for her to finish school in Oz for Christmas 2016 when she'll be 15 (right?).
Then move across the ocean to the US, spend spring semester traveling with you and settling in. (European background coloured question: what about truancy laws? Would she need to be registered as a homeschooler., and what are the requirements?)
Start in a college setting in fall 2017, when she'll be 16, commuting from home. American University is her safety for that, you will check out other unis in DC, MD, NoVa, possibly community colleges as well - which leads us right to checking things out backwards.
Going backwards, you might want to be looking at four-year-university entrance for fall 2018, at the age of 17, either as a freshman or as a transfer. Which place would be ideal? Virginia appears to have great affordable public options: UVA, Virginia Tech, William and Mary (Maryland, not so much, DC nothing).
Check out this list of colleges with the happiest students for the last five years...both Virginia tech and William and Mary come up a few times.
http://poetsandquantsforundergrads.com/2014/08/12/universities-with-the-happiest-students/If you feel she should still be close to home and cost is a factor, you should check out residency requirements for instate tuition at Virginia publics.
Then, academic requirements, both for freshmen and transfer students, and how best to fulfil these in the time you have: IB or AP classes at a public high school, entering as a junior, or community college. And then plan your move accordingly.
If she entered high school as a junior, maybe she could just pick classes she loves and/or fulfil requirements, to prepare for SATs and subject tests so she has a chance at scholarships for four year options, and maybe she would not be going crazy with repetition.
Truly complex...
