We've done this twice, with an eye to returning our DD to school the following year, when a different situation would be presented to her (full G/T services first time, G/T with grade skip the second).
Once you decide to pull the trigger, step one is to follow your local requirements for deregistering your child from public school and registering as a homeschooler.
And then step two would be to relax, and give your child a bit of space to detox from school. You're talking about a child who is already well ahead, so giving her a couple weeks' break while you get organized is a luxury you can both easily afford.
Step three would be to define your goals for the remainder of the year, because that will drive your curriculum choices. For example, I note that you said, "until next year," which would seem to me that you expect her school to have something more suitable on offer next year. It would make sense, then, to have preparing her for that situation as an educational goal.
And then, once you know where you want her to be, step four would be to assess her yourself, to see where she's at. School administrators like to kvetch about gaps, so if you plan to return her to school next year, you can start identifying any and dealing with them up front.
