As shipped the QSB can't boot from the full-sized SD card. You need to fit the DIP switch (SW1) first and then set switch SW1.2 to the ON position. Alternatively you could solder a wire between the pins for SW1.2.
I haven't tried copying an Linux image from one SD card to another, but it should go something like this:
Plug the micro SD card into a Linux PC with an SD card slot and on which you have permission to execute sudo. Wait a few seconds for the system to detect the card, then issue the following commands:
umount /dev/???*
sudo dd if=/dev/??? of=linux.img bs=1M
Where /dev/??? is the name of the raw device corresponding to the SD card slot (typically this will be /dev/sdb).
This command will take a considerable amount of time. When it finishes, remove the micro SD card and insert the full-sized SD card. Wait a few seconds then issue the following commands:
umount /dev/???*
sudo dd if=linux.img of==/dev/??? bs=1M
sync& sync
Finally use a disk partition editor such as gparted to increase the partition and file system size so that it uses up the full capacity of the card. I can't give you precise instructions here but you should be able to work it out for yourself quite easily.
When this finishes you should have a bootable image on the full-sized SD card.