The only dairy alternative that has comparable protein quality (DIAAS) is soy, and AFAIK there aren't many studies of soy milk given to toddlers/small kids.
Consumption of a mostly soy diet by small children is undesirable because of the presence of phytoestrogens in soy.
Pulses would come close second as a protein source, but a child would have to consistently eat larger servings in order to keep up with other meat-eating-and-milk-drinking children. Large portions are not always realistic in ensuring adequate protein intake in kids, who will occasionally go through phases of fussy eating.
Adopting vegetarian or vegan habits is great when periods of significant growth stop (and maybe this is what humans are meant to do, rather than to keep eating animal products in adulthood).
However, from my own experience, meat and milk is a necessity for avoiding malnourishment in little humans undergoing development.