When I move with Irresistable Faefolk to an uncontrolled battlefield and move a unit, do I become the attacker in the showdown?

Yes, you become the attacker.

According to Rule 459.2.b.1, the attacker is the player whose unit(s) applied the "Contested" status to the battlefield. When you move Irresistible Faefolk to an uncontrolled battlefield, you are the player who applies the "Contested" status, making you the attacker.

Here is the sequence of events:

1. Move: You move Irresistible Faefolk to an uncontrolled battlefield. This applies the "Contested" status to that battlefield. Because you are the one who applied this status, you gain the Attacker designation (Rule 459.2.b.1).
2. Trigger: Irresistible Faefolk's ability triggers ("When I move to a battlefield..."). You place this ability on the chain.
3. Resolution: When the ability resolves, you move an enemy unit to that same battlefield.
4. Combat: Because units from opposing players are now present at the contested battlefield, the showdown transitions into a Combat Showdown (Rule 447.1).

As established in FAQ #9423, because you were the one who applied the "Contested" status to the battlefield first, you remain the attacker, and your opponent is the defender, even though you moved their unit into the combat.