Hi Holly. I'm from the North Shore and my DW homeschooled our DD for her K year last year, so we might have something to offer in terms of parallel experiences.
My DW took some classes in early childhood development but never went anywhere near the level of a Master's degree, and though she was wracked with doubts about homeschooling initially, she did a wonderful job. I think the biggest qualification is knowing your DD and being responsive to her needs, which means nobody is better qualified to teach her than you are.
The structure can be tailored, which is one of the most awesome things about homeschooling. In DD's case, her "school day" was only three hours or so. DW would review a language arts topic with DD, and turn her loose on some worksheets that reinforced it. Ditto math. Science ended up becoming a mixture of research and art, because DW would help DD put together a book about whatever they were talking about. They spent a lot of time on biology, and so my DD has little books they made full of facts on amphibians, another on birds, reptiles, etc.
And Wednesday was art day, all day. DD loved Wednesdays.
DW found a store for homeschoolers that carried all the necessary materials, plus they coordinated certain group classes. DD took Spanish.
Oh, and you might want to think ahead to homeschooling your DD through K, too. I don't know what this gifted pre-K might have to offer, but since your DD sounds like she's already ready to graduate from K, it may fail to live up to your expectations. I can't speak to the privates, but the LA public school system makes entry into the gifted program extraordinarily difficult at age 5 or less to exclude hot-housed children who have been endlessly drilled since 2 but are otherwise ordinary in their ability levels. At that age, a 139 IQ result won't make the cut. At first grade, combined with the kind of achievement results it sounds like you should be able to expect, it will easily make the cut.
