Teach your child how to make toys and play with your cat.
A kitten or cat is the best pet to have for a young child to grow with. My first cat err Kitten, chose me when I was 3 or 4 years old. He would follow me around my Pop-pops yard. He had a few siblings but they didn’t really bother with me. One day while there he sat in front of my dad’s car near the tire like “Take me home or run me over”. He used to nap with me, and the coolest thing was if I couldn’t find one of the dolls to my doll house, he’d find them and show us where it was.
Cats are easier to care for as they are normally independent. They don’t have to be walked a few times a day and you just have to leave out a bowl of dry food and a bowl of water. Also feed them some wet food for the morning and at dinner plus of course you need the litter pan. (and to change the box at least once a week but we do it twice.)
You can make quick toys by rolling up some foil into a tight ball to play, a box (they can play in and with an old pillow or shirt can be made into a bed for them) until you can get the supplies at a store. Always be sure there’s places in the house they can climb around as well.
If you know someone who sews, crochets or knits ask them if they can make a toy for your kitten (especially one that is furry) maybe it can be made in a way that it can be opened so you can stuff it as well as putting some cat nip in it. Then you can always refresh it.
You can use some string (play with close supervision to the child and cat and never just leave the string around as the cat can eat it, and it’ll bind around their intestines and could die we know someone who’s cat it happened to)
My cats have always been part of the family, our current one is our fur baby, and spoiled by my parents. She’s been my alarm clock, she comes and gives me hugs (head butts or rubs) She knows when I need a laugh (really I swear this cat, my Sully likes to hear me laugh… She seems to forget when her tongue is out and no matter how little or far out it is always gives me a laugh. She shoots out of the litter box like a bat outta hell and runs around the house as though its chasing her. There’s are just a couple of things that make us laugh (or laugh at her).
If they are allergic to cats, get them a small animal like a mouse or hamster something furry that they can learn responsibility with then when they are around 10 or 12 then if they want a dog they should be responsible enough to care for them.