Now you're onto a subject I can really get into!
I also suggest a pop up blind like the Double Bull but there are cheaper alternatives. The cheapest is the camo cloth type blind where you just drape it over brush around you. If using a pop up, the bigger the blind the better if you are taking a kid and hoping to shoot with a bow.
I started out taking my daughter when she was 4 or 5 years old during gun season and just used the Walmart camo burlap or the other synthetic leafy cut stuff that you can get for about $15 and it worked fine. We'd find a deadfall or some brushy area and drape the camo over the branches in front of us and set up a pair of Niff-T-Seats. I'd set mine with the tall leg and hers with the short leg and put hers right between my knees. That way, she could lean back against me and if it was cold, I could kinda put my arms around her to help her stay warm.
Another tip, if you take two of the camo blind cloth pieces, you can drape one over a couple deadfall branches like you are building a fort and most likely, the first instant your kid gets bored, they'll be inside the "fort" like a dog into it's house. They can play, fidget, take a nap or whatever and you can stay on your stool and keep an eye on the woods and your kid at the same time. If you really would like to hunt for a "grown up" length of time, making the little fort and taking an old blanket along will help a bunch. Put all the blind cloths and the blanket inside a soft backpack and when you get set up, build your blind and fort then open the backpack up and lay it flat like a ground cloth and fold the blanket like a sleeping bag and put it on top. When your kid gets cranky, 9 times out of 10 it'll be because they are tired or bored. Just let them lay down and take a nap. Nothing like fresh brisk air and a soft blanket to make an enjoyable nap. I shot a doe with a 45-70 when hunting with my daughter while she was asleep in her little "nest" right beside me and she never heard the gun go off!
Be sure to clear a big area of leaves around you when you set up. That way if something comes in, your kid can move off to the side quietly. In fact, regardless of the type of blind, do a couple "pretend" scenarios. It will help them get into the whole hunting thing and it makes it a lot less likely that they screw up a situation for you if a deer comes in for real. I know we all think we wouldn't get upset if our kid spooked a deer but for some people it happens, if only for a split second before they catch themselves and tell the kids "it's okay, we'll get him next time". For me and my boy, we found that in my Double Bull, about the only place he could stand and not be in the way if I was trying to shoot my bow was to my right and kinda back in the corner. He could still see fine from there and was not in danger of being hit by a bow limb.
Gotta agree too on the snacks and drinks already mentioned, but I'll add that food and water inevitably lead to another result.... Daddy, I gotta go potty... Don't forget the TP!
I started carrying a little plastic garden trowel when blind hunting. You can dig a little hole about 6" deep about the size of a small flower pot and they can pee in it and you just drop the plug of dirt back in and tamp it down. They think it's fun! I honestly started carrying it for myself when I'd sit from dark to dark in my blind. The plastic ones only weigh an ounce or two and cost next to nothing. Of course, it goes without saying that if they have to go number 2, you either need a deeper hole or ya gotta take them downwind about 50 yards...but it's all part of the adventure.
Lastly, be sure to take your camera! Take lots of candid pictures. Get goofy and do "pretend" stuff. When you get them home and have them developed, pick one or two of the best ones and make an enlargement like a 5X7 or 8X10 and start hanging pics up an a wall in your house. I have a little section of wall in the den that is nothing but hunting/kid pictures in 8X10 wooden frames. You'd be surprised at how proud your kids will be to show people the pictures of when they went hunting with Daddy.