Well, from my limited experience since having less than 200 miles on mine (1st cargo bike) it may/will depend on several factors. If you have mostly flat ground a 1 x 11/12 system would most likely be fine, and even for some hills with the "proper" front chain ring! I tried a 30t first, it had plenty of torque, just not the speed I wanted. You will need to also take into consideration how much weight you will need to carry on those hills.
Another consideration is how big of tires you would use? I wanted 3" tires for the comfort factor and some (not real aggressive) knobbys for riding back roads and riding main roads to get to the back roads (settled on WTB Rangers). I have no plans to use this bike for singletrack. I first tried a 1 x 11/46 but in the lowest gear (or 2) the chain would rub the tire. I was told that a 1 x 10/42 may not do this, well it did, but only in the lowest gear. I could have went to smaller tires (that would probably have worked) but didn't want those.
I ended up keeping the 1 x 10/42 and used a 42t chainring. Since my bike has the Bafang BBSHD e motor, I figured I never used a 42t low gear in my life and thought I could do without it (since I had a motor). I set the rear lower limit of the cassette to stop at the 36t and run it as a 1x9. This bike is so comfortable and moves along really well on the level and down hills, on most all hills I make it up without the motor, I just go slower!
If I am hauling a big grocery order/produce or gas stove, small cooler, food & water for my wife and I to cook out in the mountains along the road I will use the motor some on the hills to help with the weight. The later is a dream we had to do together on our bikes, I built her a non cargo e bike, it doesn't get any better than this! The motor works great when I need it but try to not use it more than I absolutely have to. She uses hers more!
If you do not want to put a motor on your bike (and watch your tire size) I think a 1 x 11/12 setup should work fine for most things you will tackle. You will have to decide what kind of weight you will carry and what kind of speed you will want to go, hence the decision on your front chain ring? I wish you the best and I am sure the time you and your child will spend tougher on those rides will bring wonderful memories, have fun!