BTDT. In our district, the only way to get on the advanced math track was to start in the 8th grad. No transfers, no testing, start in the 8th grade. I have a B.A. in English for a reason. It is a 4 letter word spelled M-A-T-H.
I put my oldest in PS for the 8th grade. She struggled, but found her way, mostly b/c she was headstrong and didn't give a rat's behind about cliques and politics. She had a very strong musical ability that was not being met in our small district, however, so at 16, she moved to my parents to pursue music with my former teacher and to start college early. She wound up doing the Disney College Program and is now F/T at WDW while finishing her coursework online.
I put my 2nd DD in PS for the 8th grade. She struggled a LOT. She is a much more social creature and was much more in tune with the drama that is junior high. It was disastrous and she came back home midway through the 10th grade. Her personality completely changed and she, too, moved to my parents' at 16, but for entirely different reasons. She finally said, "to heck with it", aced the GED at 17 and started college early. She wound up doing the Disney College Program and now lives with my oldest while working P/T at WDW while finishing her coursework online.
I have to tell you, 6-8 grades is a very tough time to transition into or between schools. I moved from Germany to the US between 7th and 8th grades and it set me up for a living hades for the rest of my high school years. I *begged* to be released from my suffering. I was younger than my grade-mates and had taken chemistry and computer science in the 7th grade (back when computers used punch cards and classes were not even offered in high schools yet). Being smart didn't help me much in the game of public school.
I also used to be an English teacher for 7-12 graders and can tell you that was the primary reason I chose to homeschool. I did not like what I was seeing in the schools (the things the kids don't tell their parents about) and I did not want my children exposed to that. 7th-9th were particularly bad.
My commitment to my younger 2, now that I've been through it with the older ones is, if I can't figure out how to teach it or you can't figure it out on your own, we will find someone who can. I'll hire tutors or teachers or find a co-op if necessary.
I've said it before, my philosophy of education is simple: Wake up. Start learning. There are ways to teach different grade levels at the same time in various subjects. I think it's important not to get tied up in curriculum and schedules and keeping to the perfectly designed school calendar, but just let the kids learn at their own pace. Most people I know who are successful with multiple levels and at maintaining their own sanity and some semblance of a house with food, do so without paying attention to the outside pressures.
Now may be a good time to consider your reasons for homeschooling. What kind of compromises will you make by sending her to PS? What are the risks and what mitigation techniques do you think you will have? Is your daughter prepared for the sex, drugs, and peer pressure that are prevalent at the 7-12th (even in the 6th) grades now?
Someone once told me that this journey would never be an easy one. I would face criticism from the outside, criticism from my family, and even criticism from my children at times. Whenever I'm feeling discouraged, I remember the poem by Robert Frost, The Road Not Taken:
Two roads diverged in a yellow wood,
And sorry I could not travel both
And be one traveler, long I stood
And looked down one as far as I could
To where it bent in the undergrowth;
Then took the other, as just as fair,
And having perhaps the better claim,
Because it was grassy and wanted wear;
Though as for that the passing there
Had worn them really about the same,
And both that morning equally lay
In leaves no step had trodden black.
Oh, I kept the first for another day!
Yet knowing how way leads on to way,
I doubted if I should ever come back.
I shall be telling this with a sigh
Somewhere ages and ages hence:
Two roads diverged in a wood, and I--
I took the one less traveled by,
And that has made all the difference.