It's harder to get complete proteins on a vegetarian diet, much less a vegan one.
Basically, if you're on a vegetarian/vegan diet you aren't really getting complete proteins, so you have to rely on combining incomplete proteins to get an adequate amount of each type.
Again, I'm not saying that you can't get the protein you need, obviously you can by combining proteins if you know what you're doing, but it seems risky to have a kid on a vegan/vegetarian diet. You mess up and you could stunt the kid's growth, or worse.
Here we go again
You eat your grains, nuts/seeds, and beans to make a complete protein which you will be doing anyway if you want to be full and healthy. Secondly, you don't have to eat everything at the same time to achieve this goal. As long as you get these foods before you go to sleep, and start a new day, you are ok. Thirdly, this is actually a good thing because eating foods low in protein or in technical terms amino acids, at night allows for a deeper sleep which means a better healing of the body as the body heals itself during sleep.
That thought of needing to eat all of your beans and grains/nuts/seeds at the same time to make complete protein is old and wrong. Do more research and see for yourself that I'm not making any of this up.