As per the rules, "Men must wear full length trousers and must not wear tights." However "in Ice Dance, ladies must wear a skirt."
So no, the child would not be able to skate in the Men's category with a skirt (which wouldn't bother me in the least) but in Ladies, they can and do skate without skirts. Alexandra Trusova did so last season, unless you consider that little loose fabric as a skirt.
In the end, it yet again goes back to the stereotype that girls wear dresses and skirts.