Is a year of homeschooling an option?
The reason that I ask is that at the end of that year-- you could either place her BACK with her cohort, or you could place her in the year behind, as seems appropriate.
This side-steps the issue of whether or not she feels "dumb" or whether she is labeling herself a "struggler" or a "good student."
On the other hand, maybe give it another year in 1st and see then, with the idea of a homeschool 1(repeat) or gr2 year after that?
It doesn't sound as though her social skills NEED the school setting, necessarily, as that is a strength in spite of her age.