Atlanta Motorsports Park would be an option, however the kid karts there run the “C” track configuration instead of the full track which unfortunately skips most of the track. @Bimodal_Rocket has actually been hitting that track pretty hard on KartKraft and posting videos on another thread here, you should check out one of those to get an idea of what that would look like: KartKraft, Iracing and other sim Throwdown Season 2 - #2021 by Bimodal_Rocket
Lamar County Speedway is in Barnesville, GA and could be another good option and I know they offer a kid kart class. I don’t know what their kid kart counts usually look like, it would probably be worthwhile to ask on their Facebook page, GSKA racers seem pretty active there: https://www.facebook.com/groups/2928709867143863/
Motorsports Country Club of Cincinnati is a really nice track and might be within your search radius too. Their website doesn’t have a kid kart class listed for 2023, but they show kid kart results for 2022 - might be worth reaching out to them directly to see what the kid kart situation is over there: https://mccproamkarting.com/