The advice of the others is correct - in the classic Mac OS, the "Desktop" is not a single folder as it is in OS X or Windows. There is a Desktop folder on every disk. When you drag a file to "the desktop," by default it copies it to the Desktop folder on the same disk. Hence, when you eject the disk, you eject that disk's Desktop folder as well.
As said by others, you need to copy the file to the hard drive first - then you can move the hard drive copy to the hard drive's Desktop.