Animal Crossing New Leaf: Data transfering

You can not have multiple save files of individual towns on the same 3DS system.

Every time you save your game it generates a new, random "Save ID" and stores that ID in both the SD/Savegame and the 3DS's system memory. Trying to load a save with mismatched IDs will result in being forced to wipe the save.

This prevents two things:

1. Having two towns with one copy of the game by using two SD cards.
2. Reverting to an older backed up save to undo changes you aren't happy with.

http://gbatemp.net/threads/question-about-id-checks-with-3ds-and-new-leaf-save-files.349216/

I have personally tested this (having purchased a 3DS and transferring to 3DSXL- my game was cleared since the save data and the system ID did not match). Prior to this, we attempted backing up the SD data, erasing it from the SD and attempted a new save file on the same digital copy. This also resulted in the ID conflict. I have contacted Nintendo on this matter causing an inability to back up data. I am yet to hear a followup reply.

In the case of mismatched IDs, the game will load with a "corrupted data" error. This forces the system to erase any save data associated with the digital download- and any backed up save file will no longer work for AC:NL.

It is possible in a couple of situations, but it doesn't sound like it is in your case.

The more normal way to move is to just move. IGN has a guide on how to do that here, but to summarize, you have to have your first house payment made, have another 3DS nearby with either a physical or digital copy of New Leaf already in it, and you have to not be your town's mayor, i.e. not the first save on your game. It sounds like you don't have another copy yet though or another 3DS, and you're probably your town's mayor, so that probably won't help your case.

Another option is to download the "Save Data Transfer Tool" from the Nintendo eShop. This requires you to have a digital copy of the game before you can transfer it, but it should work even if you're mayor.

If you just want to back it up for some possible case in the future though, I think you're out of luck. Some things do have "Save-Data Backup" as an option to the left of "Manual", but Animal Crossing: New Leaf isn't one of those things.