The 1964 edition of the Official Catholic Directory (published annually by P.J. Kenedy) treats the Diocese of St. Augustine on pages 708-12.
In the city of St. Augustine, it lists the parish of St. Benedict the Moor, at 86 Central Ave., but no mention of Junior House---nor is it mentioned among the schools, convents and institutions in that city.
If you wish to do research in a library, here is a bibliographic citation :
FLORIDA. Children's Commission. State of Florida Services for Children: A Directory. [Tallahassee, 1955 or 1956?]. 28 p. (Child welfare--Florida--Directories) (a 57009273). Also: State of Florida Services for Children : [A directory, 2nd ed.] [Tallahassee, 1958]. vi, 25 p. Title cited also as: State of Florida's Services for Children. (Child welfare--Florida--Directories) (Florida. Children's Commission) (a 59009475)