You don't NEED the DLC, per say, but is it worth it? I'd say yes, totally. I wrote a blog post about this a while back:
http://forum.3dspedia.com/blog/fantasy-life-dlc.110/
I can paste you the key part:
So here's a quick list of what can be accessed from the start (or early on) and what can be accessed post-game.
Early:
More character customization
Friendship System (Friendship allows you to have better allies)
Bird pets
Post story:
A whole new part of the story with a new area called Origin Island
New materials, gear and more recipes for your classes
God rank in classes, which after allows you to have your Master as an ally
New homes and more furniture
Lunares coins currency and special items you can get from them (even new mounts, or items that allow you to change your appearance and stats at will, for free!)
Maximum level increased from 99 to 200
Level cap for the skills increased from 15 to 20
Stats cap increased from 50 to 100
Dragon pets
So in short, if you plan on buying the DLC, you don't have to wait until you completed the main story, you can get it even before starting your game and already take advantage of new features.
If you think you have enough content already, don't bother with the DLC, it might double your content but if you don't care about the game past the main story, it's not really for you.