Johanna,
There were no age restrictions of children traveling with an adult to America. In addition to all the anecdotal accounts mentioned here of family members arriving in America with children, there are hundreds of photos online showing young children with their parents arriving at Ellis Island. Women traveling alone or with children were detained briefly until a husband, father, brother or other relative could be contacted and collect them. That is what happened with my two grandmothers when they arrived at Ellis Island. This policy was enforced to protect women from falling prey to the sex trade. There were all kinds of unsavory characters hanging around the ports looking for easy targets.
Jeffrey Gee
Arizona