But you do not need to update the firmware, if you are happy with the one on your kindle, so if you give yours with 3.1 to her and you yourself the new one ..., even not sure if all new kindles are coming with 3.2.1.
But as said, with 3.1 it is easy ..., for the jailbreak take this thread:
https://www.mobileread.com/forums/sho...d.php?t=122519
br
Dietmar