copy data from public schema to another schema in postgresql

I’m creating a multi-tenant RoR app using PostgreSQL 9.3.5 running on linux (Ubuntu 14). I’d like to copy the data from my public schema to another schema.

I tried:

pg_dump -U my_username -h localhost --schema=public -d my_db -Fc -f db/my_dump.backup

pg_restore -U my_username -h localhost --schema=my_schema -d my_db -a db/my_dump.backup

It does not copy the data from the public schema. Any thoughts?