I actually found a little article on Jane Doe! I believe Sharon said something about it either in an interview or the fan-club magazine. She said she really likes murder mysteries, so she wrote this song in relation to that, as an episode. It's basically about this psycho killer who tells his new girlfriend about all the bad things he's done, and then she laughs at him. So he kills her and attaches a bag of stones to her body and drops her in a lake. However, the bag wasn't tied tight enough and she started floating, so it's only a matter of time before he is caught!
And, for the record, a Jane Doe is a female who can't remember who she is or whose identity is unknown.