Poor little darling. 😥
I was responsible for the death of a pet too when I was a teenager. I will always carry the guilt of that.
It's very hard to know what to suggest. Here are a few ideas for the death of a pet generally:
If you have a garden, go to the garden centre and pick out a tree to plant as 'her' tree, maybe over her grave if she has one. Remind him how important trees are for all living things on the planet, and you wouldn't have bought the tree if it hadn't been for losing her, so her life has caused the planet to be that bit more of a better place.
When the time is right, go through her belongings and see if any are donatable to a rescue centre. Again, stress how, because she lived, other dogs can have abetter quality of life.
Suggest he write her a letter. He can burn it or bury it, or keep it if he prefers. I found this very cathartic when I was young.
Don't lie to him (he'll see right through it and will lose trust/respect for you) but it's ok to say that as the adult it was your responsibility to double check the gate. We're human, we make mistakes.
A weighted blanket or weighted cuddly might help, or taking one of her soft toys or blankets to bed with him.
Have a look on YouTube for child friendly videos on grief that you can watch together.
Don't not talk about her. My mum wouldn't talk about our dogs after they died and I found that so hard, because I desperately wanted to.