can i transfer my backup to another computer and then restore my backup

Yes. However, the backup file does not necessarily contain everything on your device (music, some purchases, some photos) so you want to make sure all items are backed up and transferred for safekeeping first.

iOS: How to back up - http://support.apple.com/kb/HT1766

iTunes: About iOS backups - http://support.apple.com/kb/HT4946 - including a list of what is backed up.

How to Restore iPhone From Backup - http://ipod.about.com/od/iphonetroubleshooting/ss/restore-iphone.htm

iTunes: Backing up, updating, and restoring iOS software - http://support.apple.com/kb/HT1414

You will need to copy the backup file from one computer to another:

http://support.apple.com/kb/ht4946 - iTunes: About iOS backups > Where iTunes backups are stored on your computer

Read here.

https://discussions.apple.com/thread/2431472