So far, we've unlocked the following:
Day 3: You can change her jobs after this.
Day 6: You can change her weapons after this.
I gave my NPC a great sword just for kicks, and it's pretty funny watching her walk around with a giant black sword. I may change this to great katana or great axe just for kicks though. I may even give her an axe.
Confirmed info: Apparently fighting mobs higher level than her gives her more XP, no matter what your level is. My NPC hit LV31 two days leveling with my SAM after 4 days leveling with my NIN.
I imagine depending on what you fight, she levels up much quicker. This is great for people who have multiple high-level jobs. You could farm higher level mobs all day (say, LV50-60) and you would level her far more quickly.