Apparently you cannot just paste an image into the editor window. Instead you need to add a toolbar icon to insert an image which uploads the image to the server.
Since I don’t want to have to manage uploaded files I opted to add a facility to attach a file to the email.
This can be done by adding a File Field to the form by using Insert/Form/File Field in Dreamweaver. The user can then use the browse button for the File Field to select the file to be attached.
Then by editing the server behavior for Universal Email, you can reference an attachment to that File Field.
The advantage is that any file can be attached to the email, and nothing is uploaded to the server.