There are two options:
Open the compose window for the new email, then drag-and-drop the old email into it. Note that you need to drag the old email to the attachment area of the compose window (to the right of the address fields in the default config). Dragging to the email body does not seem to work.
Save the old email to a file (select old email, then File/Save as.../ save as .eml file). Then attach the file to the new email like a normal file attachment - Thunderbird will automatically detect that it's an email, and will attach it with the correct MIME type message/rfc822.
And BTW: It seems you're not the only one who has trouble finding this feature. There is an enhancement request to add an option "Attach email" to the attachment button: https://bugzilla.mozilla.org/show_bug.cgi?id=380256