I think I disagree with you, it's not a rule, but a family will and wish.
Usually at Catholic funerals (and I've been to a lot), children are dressed in dark colors just for the respect of the deceased and other people, if they choose black, dark blue, brown, dark green, etc... is up to the family to decide what's better and appropriate. Princess Elisabeth and Prince Gabriel wore black for the funeral of their maternal grandfather, there's nothing wrong with black.
My country is Catholic, and I never seen white at a funeral so far, but it depends on the country traditions and the families will.