As you say, what you want to do has to be done from dos. Most, if not all, retail boxed HDD's will come with a utility to copy the contents of one drive to another.
As your new disk did not your best bet would be to visit HDD's makers web site, and download the software they normally ship with a new drive. For example click here if it's a Western Digital one.
Once you have the relevent program's, it's just a case of following the onscreen options. One of the options will be somthing along the lines (obviously) of 'copy disk'. Be very careful to copy the right way round, or you will end up copying off the new (empty) disk onto the old one.