You are correct, Gwenio. You need to fulfill each fortune to get another from her, and after a doing another couple, the next fortune is what scares her off.
The white rabbit can be seen in a cutscene if you walk down the river bank from the fortune teller (if you get to the rocks with the iron ore deposit, you've gone too far). The rabbit leads you somewhere nearby, where you can find a chest with random loot (nothing special, though).
