Replace old WD Passport Question

I use an iMac with OS X 9.2 and the iMac is about 5 years old and have been using a WD Passport all that time for backup through Apple Time Machine.  One of the benefits of the Passport is it has all the old material still saved (by date) that had been backed up.  If I purchase a new WD Passport can I transfer all the old saved files on my old Pasport onto the new Passport so I do not loose any of that history?

I would assume just copying it over, the folders I mean, into your new drive would be just fine.  Then you can continue to back up the computer using Time Machine like you normally do.  

Thanks for your response.  

But the problem I am concerned about is that the old Passport drive has each backup on it separately since 2010.  In the past I have been able to go back in this history when I had inadvertently erased something to find it.  I have also use Carbonite on-line back up but it only keeps what you have backed up last (items deleted are removed from their backup file after 30 days by Carbonite if they are not on the last backup).

So I would rather not loose all these past “backups”.  I do not know if they would still be saved because I use Apple’s Time Machine or if they are just on the Passport drive.

I am concerned also that this old Passport will fail as it has gotten older so that is why I am looking into getting a new one.  I may not be able to solve this dilemma and just bite the bullet and get the new Passport.

Any suggestions?