Assuming you have emuNAND installed, you will have to transfer that to the new SD Card before transferring the files.
1. Save all the contents of the old SD Card on your PC and dump the emuNAND with emuNANDTool.
2. Place the newest Gateway launcher on the new SD Card and insert it into the 3DS. Boot into Gateway and format emuNAND.
3. Next, connect the new SD Card to your PC and inject the old emuNAND with emuNANDTool.
4. Finally, move all the contents you saved to your PC to the new SD Card.