Can I set a password on an existing dmg?

You can change it by first selecting the DMG in Disk Utilty. Then go to Images>Change Password.

Change Password - Disk Utility
It will prompt you for the password. prompt for password - Disk Utility
Then, it'll ask you for a new password for the DMG. New password prompt


Open the Terminal application, and type

hdiutil chpass <image>

where <image> is the disk image path. You can type "hdiutil chpass " and drag the file to the terminal window to complete the path. The disk image need not be mounted. The command will prompt you for the current password, then for the new password, followed by the new password again for verification.