You have a full backup of size 1GB. Create a database on the QA environment with the same logical file name as of the Production DB. Restore the database and then shrink it.

Script:

RESTORE DATABASE [DATABASE_NAME]

FROM DISK = 'Path_of_the_backupfile',

MOVE 'Logical_datafilename' TO 'Physical_datafile_location',

MOVE 'Logical_logfilename' TO 'Physical_logfile_location',

REPLACE

GO