Since you're homeschooling (essentially), I would call him what he is (a kindergartener), and allow him to do whatever level of academic work that is appropriate. If the online school won't allow this, I would consider homeschooling independently.
At 5, my son tested into K12's 2nd grade language arts. I used it for about 4 months and it really helped me to place him in the different LA areas the next year (much more so than a placement test would have done).
From K-4 he was always running 2-4 years ahead (and mastering the material), but on paper we kept him at grade level. This year, he is going to a private school, and so we had him skip 5th and did an additional year of math acceleration. Academically, it is still not enough though managing his stuff (books, notebooks, papers, jacket, lunch, etc) is a bit overwhelming, it seems.
Anyway, my point is that I'd wait to officially advance him until he enters a brick and mortar school and you know what his needs are at that point.
