I think pickiness has a lot to do with the fun factor. I had friends from the UK visiting me in Canada, and took them canoeing on our suburban bay. They asked how often we did it and I said hardly ever. If I go canoeing I try to go to a new place I haven't previously seen. Your first trip will be an adventure no mater where you go, after that you will likely get progressively picky.
The only thing that would worry me (I have three kids) is the ability of your kid to enjoy the trip, stay in line, and not get spooked in those conditions. The real chance of being nailed if you don't do something unpredictable is pretty near zero. If you get hit by a car doing 35 MPH in your regular cycling, granted the energy level is much lower, but it isn't something you would enjoy, or likely survive. There are less distractions on country roads, and people know a deer can appear at any moment, and they don't want their cars hit by a 200 pound object moving at 55 either (you and your bike). You and the car are in this together. Is it safer than skateboarding in a skatepark, probably.
Local culture can have an effect, the Easy Rider factor. If you think your area isn't bike friendly, you might consider something placating like a support the troops decal. My main experience in hick areas has been excess courtesy. People moving out of the lane entirely. It does make me wonder how confident they will feel squeezing by me if they encounter a logging truck coming the other way. Bike touring is essentially safe, given average conditions. That said, if you can find off-road snowmobile trails (
), horse trails, atv trails, that you could do the whole tour on somewhere, all the better.
Develop a bottom line attitude. What is the worst that can happen and what do you do then. Don't develop the attitude that if a car comes too close you can't hop into a ditch, or position yourself out a little to slow traffic for your kid, etc... I wonder how many normal car accidents occur because someone is holding a cup of coffee and doesn't want to ruin their suit by dropping the cup and taking full evasive action. Always strategize your out. Harder to draw kids into it though.
There is also the practice vs. performance thing. A lot of people try to do something before they get the practice in. I don't actually think cycle touring needs practice for some people, but others may find handling gear weight on the bike, or in your case riding in higher speed traffic is something they need to try first. Presumably you haven't done it because it concerns you, but you are going to have to do it for this trip and there will be other dynamics and factors in play then. You should consider going out for a test bike ride yourself, then going out with your kid for one. Then doing some riding with loaded bikes, and so forth. Rather than having a potentially dangerous situation on a trip when you try half a dozen new experiences all at once.
I was experienced in bike touring when I tried out my then new bike a few years back. At one point I had to cross the road to go to a store, and I hovered track start style, then wheeled out into the road to catch a short break in the traffic. That was when I discovered I had toe overlap with the front wheel and almost landed sprawling in the traffic. No real problem, but I would not want to see that video in my head for one of my kids because I didn't do my homework. How we prepare is part of the lesson we teach our kids. End of sermonette.
One thing people like are those handlebar mirrors, or helmet mirrors, so they can keep an eye on traffic coming from behind. I'm not a fan, but you might like them. One thing I do for fun is ride the line on the edge of the road. On some surfaces it rolls a lot better, and like riding rollers, you learn to keep the bike really on line. This would be good practice for your kid before go out there. Learning to keep a very straight line is a good safety skill. I'm not sure i could do it while checking traffic in a helmet mirror.