Hi,
You can go ahead and proceed to move to 2.5.1 from 2.5 with the same license file.
License file for your version 2.5 will work with 2.5.1.
Regarding your database you can take a backup by using GSS backup_db.wsf in the scripts folder.
which will create a backup on your My Documents in the folder name GSS_BACKUP.
Later you can restore the database by clicking on retore_db.wsf.
Thank you
Sockkalingam.S