I love that dress. It's really cool looking. I like your idea of a post-apocalyptic time traveler. You can mix all sorts of little trinkets with the outfit from different eras (I've thought about this a lot since I was working on a design for a time traveler at one time) and have like a backpack to carry stuff in. Maybe a journal that looks worn and old with lots of different stuff in it.
As for the skirt, you could pair it with a white button down shirt, maybe a corset over it or a leather jacket. You could wear some nice boots with it and maybe a Victorian inspired hat...that skirt could be punked nicely with stuff you can find in thrift shops or around your house.