I'm looking all over the desert for the beast that needs to be dispelled, but it's just not there. I'm on day 3. Is that too early? I've been looking at maps online and it's simply not there.

You are looking to early.

You have to wait until day 14 or something. You will know because when you go out, the guard guarding the entrance of the city tells you that "The Dervish" wants to speak with you.

The beast appears after you defeat the Earth Elemental. It's not possible to gather the final ingredient for the dispel potion before this point anyways.