Akali move to a battlefield with a move effect and deal 1 damage. Defending was a Teemo Strategist with when I defend trigger. Which should resolve first?

Yes, Akali's move trigger resolves first — well before Teemo's defend trigger even becomes pending.

Here's the order:

1. Akali moves to that battlefield. Her "When I move" trigger fires immediately.
2. That move trigger goes on the Chain and resolves completely (dealing 1 or 2 damage if Empowered).
3. Only after that chain empties and a Cleanup runs does the Showdown officially begin. Teemo gains the Defender designation at that point, and his "When I defend" trigger becomes pending.

So your Akali can deal damage to Teemo or another unit at the battlefield before the combat starts and before Teemo's defend trigger has a chance to do anything. If Akali's damage kills Teemo in step 2, he won't be around to defend at all. (FAQs #4077, #10571)