Games have to pay attention to modern sensibilities, but in the Wasteland if you are able to do a full days work and pull your weight, then you are advlt.
People may not give you as much respect as Grand Ma Hackett, but she has lived four times as long as you.
Come back when you have a little more of an advlt track record.
With civilization, we have the luxury of letting our kids have an extended childhood, but the equipment is all there because for the longest time we didn't have the luxury.
Or I'll put it this way, if you are in the Wasteland with a spare rifle and ammo and have a 14 year old boy traveling with you, would you or would you not all things being equal, give him the weapon to carry?
I wouldn't let him out of my sight until I was sure he could handle it, but I wouldn't have let him out of my sight if he was unarmed.
And I certainly wouldn't let a girl go unarmed if I thought she was old enough to be able to handle it.
I think Bethesda is handling it right by having little kids and older teenagers and skipping the tweens/preteens/young teens.