Ah, I spent many hours Googling this yesterday (inadvisable, I found out so much stuff that would put me off even buying a 3DS, so please don't google this!).
The answer you got is correct. System transfer and then once it's complete, pop your existing SD card into your new 3DS and you're set. It's at this point that you can upgrade to a bigger card if you wish, I'll include a couple of links that I kept for use.
System transfer:
http://www.nintendo.com/consumer/systems/3ds/en_na/ht_apps.jsp?menu=transfer%20games&submenu=ctr-ht-software-transfer
If anyone wants to upgrade SD card, this is helpful too:
http://lofi-gaming.org.uk/blog/2012/01/19/how-to-upgrade-your-nintendo-3ds-sd-card/
I heard it can take up to 45 minutes for a system transfer and the same again to download the game. The system transfer will delete all the data from your old 3DS and transfer it to the new one but keep the eshop account info, so it'll see that NL was on there and let you download it again for nothing onto your 3DS!!
Do you mind if I add some questions I have into here too??