I have two kids ... my older has a late spring birthday, and my younger has a fall birthday (just missed the cut-off). I too had thoughts that the younger was going to be _so old_ when starting kindergarten, but now that the time has come, I don't feel that way at all. In my younger's pre-k class of fifteen kids this past year, there were four red-shirts, and my child was only the sixth oldest in the class (with other fall and winter birthdays). My child is definitely in the right cohort.
That being said, some private Ks will take very young kids (and after doing private K, you always have the option to then go into FCPS K the next year). But personally ... I would focus on looking for a good pre-k or junior kindergarten (or head start, if you qualify) that gives your child the challenge/stimulation needed but keeps them with their cohort, as a Dec. birthday (even in a non-Covid year) will likely be toward the middle of the class age-wise.