I would give children the penalties for being one step smaller as given to an animal. This would mean a hilariously low strength score by default, actually. But it could theoretically work.

Children really shouldn't (with rare prodigal exception) have a PC class. I imagine they'd be stated like commoners.

Perhaps... Keep going with the age categories in the DMG? Of course, children wouldn't have higher physical stats than adults... Maybe -2 str, -2 con, -2 int, wis, and cha?

Maybe. I don't know.