I am using Carbon Copy Cloner to backup my MacBook. Any suggestions on how to confirm the stuff is there?
You bet. First of all, whether you are using it manually or on a scheduled basis, you'll get an error if things don't go well. You can go to the Window menu and to CCC Log, and while the log might look a little geeky, you can see if there were any errors.
Also, open external the hard drive on your desktop, go into Users, then into your home folder (probably has your name on it). Go to the View menu and view as List, then click at the top of the Date Modified column to sort the folders in date-order. If you see files with the same date as your last backup, you should be golden.