How to append a date in batch files

I have the following line in a batch file (that runs on an old Windows 2000 box):

7z a QuickBackup.zip *.backup

How do I append the date to the QuickBackup.zip file. So if I ran the batch file today, ideally, the file would be QuickBackup20090514.zip.

Is there a way to do this?

Bernhard's answer needed some tweaking work for me because the %DATE% environment variable is in a different format (as commented elsewhere). Also, there was a tilde (~) missing.

Instead of:

set backupFilename=%DATE:~6,4%%DATE:~3,2%%DATE:0,2%

I had to use:

set backupFilename=%DATE:~10,4%%DATE:~4,2%%DATE:~7,2%

for the date format:

c:\Scripts>echo %DATE%

Thu 05/14/2009

This will work for the non-US date format (dd/MM/yyyy):

set backupFilename=%DATE:~6,4%%DATE:~3,2%%DATE:~0,2%
7z a QuickBackup%backupFilename%.zip *.backup