It really depends on the child
General rules, for young children, are to be more relaxed with the rules - lean heavily into rule of cool and go very light on punishing mechanics. When I've run for my youngest nephew I've used more gut feeling than stats like HP or AC, in fact I don't like to track HP for them at all - introduce that as they get older.
- Retaliating against them in the world with things like getting stuck and needing to get out of a net, as opposed to knocking their character unconscious.
- Tell them the number to roll higher than when they're attacking. I don't know how good your four year old's maths is but I found not giving them any pluses to rolls worked better. Just saying "Ok, you're pushing against that box to move it, but let's see how hard you push - this is quite a heavy one, but your strength is good so you need to roll over a ten to get it out the way." Rather than the DC being 14, but they have +4 to strength.
In terms of the actual array for stats, talk to them about it. Do you want your dog to be a big strong one, are they more clever? Then pick skills that compliment that.
I've run games for my nephews and, though they're a little older, I've found the key is always getting them to like their character. I recommend getting a mini of them (this could even be one of their existing toys) to give them something physical to relate to. Good luck!