The backup file you made is simply another wallet.dat file with a new name.

To use your backup in a fresh install of Bitcoin-Qt:
-Shut down Bitcoin-Qt
-Find the wallet.dat file from the fresh install. It's usually located somewhere in C:\Users\Your-username\Appdata
-Delete the found wallet.dat file
-Put your backup in the folder where wallet.dat used to be
-Rename your backup to wallet.dat
-Start Bitcoin-Qt and it will use the backup as your current wallet, including it's contents