Mount is what you want. You don't necessarily need to burn all dmg files. eg: LimeWire is downloaded as a dmg file. You simply open it & open the installer inside it. Mounting the image puts it onto the desktop. It mounts just like a normal disk does. And to be rid of it, you drag it to the trash or select it & press command E or Y.

I doubt you don't have Disk Copy. Go to the desktop & press command F. Then in the search engine type in Disk Copy. You will find it. I run OSX 10.4.6 also & I have it. If you arranged your utilities folder alphabetically or viewed it by list instead of by icon then you'd probably find it.