Hey Emu,
I did some searching, and here's what I found:
First:
This guy describe solutions to backup an SD card without a computer. The main one is a $90 product that I think does some of what you want, although I'm not sure.
The second option is something like this:
It's a DIY solution that appears to do exactly what you want, although the main component looks like it's out of production, and the main replacement is $55, which is kinda pricey before we even consider making a case and battery and such.
There are some other DIY possibilities, but before I dove into those I came across this:
It's an iPhone-compatible SD card reader. Would that work?