I know this is slightly different thing but I'll tell you anyway!
I sent my Rutles video cover to Eric Idle to sign (an address in the UK). So I basically done the following:
Used an envelope that was roughly the same size as the video cover for sending it to Mr. Idle, and I also included the same size envelope for an SASE. I also included a piece of card to keep the video cover safe from bending.
That's basically it and my cover came back safe, sound and (of course) signed!
Dakota Fanning is a very good signer (I believe) so I shouldn't think there is too much risk in sending your DVD cover.
So, hope you understood all this and good luck with getting a reply!
Paul
P.S Let me know if I haven't answered all your questions!