Whether a vegan diet is unhealthy for children or not, this isn't how you study the question:
Putting children on strict vegan diets is "unethical" and could harm their development, a US scientist has argued....Research she carried out among African schoolchildren suggests as little as two spoonfuls of meat each day is enough to provide nutrients such as vitamin B12, zinc and iron.There are - how can I put this delicately? - some serious methodological problems here. You'll note that Allen - whose research was conducted under the auspices of the USDA - attempts to draw some convoluted equivalence between malnourished African children (who fare better when they're given more food...I'm glad that Science has finally sorted that out!), and first-world populations wherein a vegan diet need not be limited to "starchy, low-nutrition corn and bean staples lacking...micronutrients."
The 544 children studied had been raised on diets chiefly consisting of starchy, low-nutrition corn and bean staples lacking these micronutrients.
Over two years, some of the children were given 2oz supplements of meat each day, equivalent to about two spoonfuls of mince.
Two other groups received either a cup of milk a day or an oil supplement containing the same amount of energy. The diet of a fourth group was left unaltered.
I'd further suggest that an experiment which relies for its dubious efficacy on witholding food from already undernourished children is, in itself, unethical.
As for whether a vegan diet is healthy for children...I have no real opinion, except to say that it's probably no more unhealthy than what the average American child eats. If it's "unethical" to feed children badly, that's yet another good reason to get fast-food vendors out of America's schools.