I'm only partially deaf but it does make me a lot more careful when I am out and about. Even so, I have been caught out by a pedestrian when I should have been perfectly safe. I've had a near miss with a bike too, but this was a full grown man cycling the wrong way down a one way street and insisting that the one way rule only applies to the direction of cars, not cycles.
At busy times everyone should be more careful when the step out of shop doorways. Pedestrians can be just as dangerous while walking as bikes or dogs or mobility scooters etc. I can't remember how many times people have stepped out of a shop in front of me and we've nearly collided.
While I was very heavily pregnant with my son I was standing looking at a shop display, inside the shop which was used as a cut-through from the shopping centre to the street outside and a man approached from my 'deaf side' and knocked me down.
He was walking, I was standing still, but he was in a hurry and not looking where he was going, I was focused on the things I was looking at and didn't hear him coming.
I was on the floor, crying, with an injured arm, a massive pregnancy bump and wearing a bright red coat. He should have seen me before he hit me but he didn't. He didn't stop to help me either, he just shouted "I'll miss my bus" and carried on.
I know the crying was an overreaction but I'd already lost two babies and I'd fallen forwards, twisted sideways and (luckily) my arm took the impact but I did bang my bump on a shelf as I fell. I was convinced he had harmed my baby for the sake of not missing a bus and so yes, I cried. I was scared and in pain.
Nobody came to help me, not even the shop assistants from the till nearby.
So I know from bitter experience that pedestrians can be just as dangerous and you are not even safe when you are standing in plain sight.
I've also been bumped by an old man on a mobility scooter while I was standing in a cash point queue. He sounded his horn, which was a tiny little "peep-peep" noise. I heard it but it didn't register with me that it was from someone behind me wanting to get passed me. I thought it was a noise from the ATM. He could have spoken and if he had said "excuse me" it would have registered with me and I would have moved. You expect people to say "excuse me" on the pavement, not sound a little peepy horn at you without speaking. So I didn't realise what it was, hadn't even heard the scooter come up behind me, and I didn't move. He chose to hit me with his scooter rather than speak to me and when I asked him what he was playing at he said "Didn't you hear the horn you deaf cow?" and drove off, leaving me muttering "half-deaf cow" and rubbing my sore leg.
Perhaps you don't need to hold your sons hand all the time OP but he does need to be more careful than most, because although you should be able to rely on others to watch where they are going or take care of those around them, you can't. Not if you can hear perfectly and not if you have a hearing impairment of any sort.
And the good thing is, it sounds like your son knows this and reacted exactly right. He saw the danger and reacted properly, stepping back out of harms way with no injury to himself or the little girl.
Someone has posted the view that the law takes on young cyclists and as this girl only looked to be about ten it doesn't appear she was breaking the law even if you are right and in every other way she was too young and too fast to be out alone and on the pavements.
But if you are still concerned about the safety of pedestrians from cyclists on that stretch of pavement you can report the incident and your worries on here and your local council will be informed.
I'm glad your son is okay.