How can I transfer my New Leaf data to a new console?

What you need to do is a System Tranfer

And Nintendo says in their guide

Pre-installed games, such as Monster Hunter 4 Ultimate, will be available to redownload from the Nintendo eShop on the target system after the system transfer has been completed.

Here you can watch a complete walkthrough on how to perform a system transfer.

Keep in mind that when you do a System Transfer, your Animal Crossing 3DS must be logged to your Nintendo Network ID and your Zelda 3DS must be without an account. If the Zelda 3DS comes with a pre-loaded game, log in with your NNID to link the game to your account, then format it and proceed with the system transfer.

Some things to have in mind while doing a system transfer are specified here

For the most part, information on the target system (system being transferred to) will be overwritten by the information on the source system (system being transferred from)

• Save data associated to DSiWare and Nintendo 3DS Downloads
• Data associated with any pre-installed applications (Face Raiders, StreetPass Mii Plaza, etc.). Only the data associated with the source system is retained.

  • Pre-installed games (Mario Kart 7, Super Mario 3D Land, etc.) are treated as a standard Nintendo eShop game license. The license will be on the target system once the transfer is complete

Here is a picture that shows in an illustrative what is transferred and what not

Source

So all your saved data will be transferred to your Zelda 3DS XL, but keep in mind that all of your data from the Animal Crossing 3DS XL will be erased but accesible from your Zelda 3DS XL (audios and photos are the only exception, so make a backup of those before transferring).