I can give the OP some anecdotal information about my eldest, who is a boy and is 14. He skipped two grades and is now a combined high school junior/college freshman. This odd placement is because he's enrolled in a program called Middle College. I recommend that others at least read about Middle College programs. They're fairly popular are free, and aren't heavily advertised.
Academically and socially, the double skip worked out well through 7th grade. Eighth grade was difficult for him socially for a variety of reasons. One of them was that the boys were adolescents and he wasn't. He homeschooled for 9th grade and then went to the regular high school last year. At that point, he was bigger and he fit in better with the boys in his class, and always had someone to hang around with at lunch, etc. He was happy last year. He's also happy this year, though the girl thing is probably tough. That area is presumably tough in its own way for 99.9% of high school kids, though, so at least he's in good company.
Middle College (MC) is a dual enrollment program for high school students (some programs are for grades 9-12; more typical is 11-12). Academically, it's amazing at this point (>3 weeks in) and has surpassed my expectations. People who read this forum regularly know how often and how loudly I complain about schools, so for me to say "it's amazing" says a lot.
My son spends his whole day at the college, where he takes 3 high school classes with the people who run the program, and and 3 college classes. Interestingly, the MC students aren't allowed to take remedial courses! He may have an A.S. in Mathematics when he's 16 (hasn't completely decided yet). The people who run the program are very smart, and that makes a huge difference --- not just for my son, but for all the kids in the program.
Others here have said, "We don't want our child to go to college when s/he's too young," and I understand that sentiment, because I feel it too. My concern is that being too much younger than the people around you will create significant social problems. So far, Middle College is allowing DS to take college classes while being surrounded by students who are still kids. He also benefits from the college's open-minded perspective regarding very young students. For example, a 12-year-old took calculus recently, and there's a 13-year-old non-Middle-College student in one of DS's classes.
Middle College programs presumably differ from place to place, but they're generally seen as alternative ed. From what I've seen, programs in this bucket tend to have increased flexibility and less of many of the very frustrating stuff that comes with big public school systems and even many private schools.
