Although I generally agree that this system has some severe flaws, here's a couple questions to see its merits.

Are you augmented the system so that all adult humans have 2d8 racial hit die on top of their class level hit die? If yes, that solves the issue of children being more resilient than a level 1 <most classes>. Also, if orcs and other races also keep their racial hit die from being an adult, that solves the issue of a child army being stronger than an orc horde.
Additional reason to keep the racial HD if you include this change: You can explain spellcasters losing HP by their poor health choices to get mystic might--BUT that goes against the idea of HP incorporating luck, divine favor, and other non-physical aspects (which is fine, several folk disregard that). However, 2d8 averages 9 HP. That's more than a level 1 cleric gets, and they are a combatant-like class. If rolling for HP, a fighter would average around 5-6 HP and a barbarian around 6-7 at level 1.

However, I think most of the issue would be resolved by having the child be a level 1 commoner with reduced HP, as others have mentioned, instead of using racial hit die. Racial hit die seem reserved primarily for monsters (or 'monsters', in the sense of not normal PC races) that may or may not have classes. The common humanoids use class HD instead of racial HD, and humans default to the (admittingly weaker) Commoner instead of Humanoid.
Using the commoner template (with penalties for the very young) fits the rest of the game better, requires less augmentation of HP across the board, and seems to make more sense.