There is no easy way to do this in cPanel, therefore, you'll have to get your server admin to do it, however this is what you would have to do:

Create the database Database1, then log in to your server via SSH, issue the following commands:

mysqldump -u root -p Database1 > Database2



When asked, enter the root password, than issue this command:

mysql -u root -p Database1 < Database2.sql



Basically you just copied (or dumped) the data from Database1 into a text file, than inserted that data back into Database2.

Very quick and easy task.