Story, not Rules.
Fail Forward.
Die rolls should be dramatic (even if they aren't, make them seem that way).
Pets is an awesome suggestion. I used our pet dogs as giant wolf companions when I played with my son at that age.
I took a Zelda dungeon layout and put Basic monsters in it (copying when I could, such as the bats in the undercaverns) for my son's first D&D session. Pre-gen characters (the 4 original classes). Magic item directly helped beat the BBEG - Skeleton Dragon that "breath weaponed" a string of knuckle bones at you. It did not at all appreciate being smashed by the +1 Mace after being shot by arrows and taking half damage because skeleton.
Next up (but not played because he figured out 3e rules) the "Swordswallower" dungeon - BBEG was a Rust Monster.
Thanks for the advice, everyone. I don't know if it's of interest to anyone but I've...slowly and intermittently...begun my kid campaign. My nephew insisted on played a premade adventure and starting at level 1, so I adapted the Sunless Citadel (from TFTYP) with a number of changes. My niece really liked the picture from Xanathar's Guide to Everything of the Shepherd druid with all the wolf puppies, so decided to play a druid with a litter of wolf pups as pets. I gave her two shiny glass beads to represent spell slots. My nephew is playing a rogue (with the intention of going arcane trickster) with an apprentice rogue minion following him. I gave the apprentice rogue 5 hp and a +4 attack bonus; making him vulnerable but still useful; and unlikely to outshine my nephew's character. My nephew controls and rolls for him when he chooses to but I roleplay the minon. The nephew immediately (and wisely) tricked out his apprentice with a shortbow. The wolf pups are too young to contribute to combat, but they're alert to danger and are decent at tracking things when I feel the need to pull the youngsters in a particular direction.
The game started with about half of my niece's wolf pups being kidnapped by a mysterious, tiny, assailant. Which later turned out to be a goblin.
One wolf pup was found at the bottom of the chasm where the Sunless Citadel lies
The goblins in the citadel worship an evil demon death-chicken. They've been collecting sacrifices (like one of my nieces' wolves) to give to it. I'm not sure how I'm going to ultimately handle this; but I might replace the ultimate outcast druid villain with some sort of giant chicken monster on the final level. Or just have it be a minion of the evil druid.
The goblins have been vandalizing the citadel's dragon imagery, trying to make it look more like chickens. The kobolds have been trying to undo their efforts.
The kobolds managed to capture one wolf pup who chased the goblin kidnapper into the citadel. They intended to eat it but are willing to trade it back to the niece's druid in exchange for returning their dragon wyrmling, Calcryx.
The kids have really loved Meepo (who I'm keeping in reserve as another minion if it turns out they need it) and tricking incompetent goblins.
Unfortunately we haven't had much playtime, since the two are usually accompanied by a 4yo sister who requires a lot of oversight and doesn't have the patience for the game yet.
