There are two  methods for taking backup of a single table from a database and restore in into another database

1) Method 1

In this method you can take  a backup of a database table and  restore into another db. But this restoration will remove the  already existing  table and recreate it in the new database .

#  mysqldump old_db table  > old_db.table.sql
#  mysql new_db < old_db.table.sql

2)Method 2

In this method you can table only the backup of database table  data ( not the sql scheme )  and restore it into new database without removing the old data in new database

#  mysqldump -t old_db table  > old_db.table.sql
#  mysql new_db << old_db.table.sql

Make sure to table backups of new database before doing the restoration