You can achieve this by simply creating a batch file to run the copy command, and generate a folder name using the date in a parameter.
Here's an example (from my own backup script). I've assumed that the date format is DD/MM/YYYY. You'll need to experiment with that. Also, my K: drive is the backup drive.
Set mm=%DATE:~3,2%
Set dd=%DATE:~0,2%
Set yyyy=%DATE:~6,4%
@echo off
if exist "k:\Backup_%yyyy%%mm%%dd%\filetobackup.txt" (
echo %yyyy%%mm%%dd% - Log File Exists >> c:backup_log.txt
echo %date% %time% - Cancelling backup process. >> c:backup_log.txt
exit
) else (
mkdir k:\Backup_%yyyy%%mm%%dd% >> c:backup_log.txt
k:
cd k:\Backup_%yyyy%%mm%%dd%
xcopy c:\Backup\filestobackup.* k: /j /v /y >> c:backup_log.txt
echo %date% %time% - Stopping backup process. >> c:backup_log.txt
exit
)