How do the college's A level results compare with other schools? My DS2 goes to a local college that has a sixth form as well as vocational courses and while it suits those DC who might not have enjoyed school, in that they're treated more like students than pupils, their achievement is lower than mist local sixth forms. That said, I haven't checked their progress figures and the fact that there are lots of school sixth forms locally means that they have perhaps a lower achieving cohort. Your local college may be the best option around for state school pupils.
I wouldn't like the idea of a class with only 1 student. What subject is it? If it's one that would benefit from throwing ideas around like philosophy and ethics etc, then I'd say it's a definite 'no.' We have chosen a different sixth form for my DS3 partly based on the low numbers taking FM, 3 in current Y12, as that seemed too small to make for an adequate experience.
I know nothing about private schools, personally, but my good friend's DS left one in Y11 down in Cornwall to go to Truro college which is huge and loved it. He did well and is now at uni. He didn't seem to get any stick for being an ex private schoolboy.
What's your DD like, shy or extrovert?