If I am moving a Stellacorn Herder to a battlefield, does my opponent have a window to gust Stellacorn before the move trigger resolves?

Yes, your opponent has a window to play Gust to return Stellacorn Herder to your hand before its "When I move" trigger resolves.

The Timing Breakdown

1. Movement is Instantaneous: According to Rule 441.3, moving is instantaneous and cannot be reacted to. Once Stellacorn Herder begins to move, it instantly arrives at the battlefield destination.
2. Triggering: Once the unit arrives at the battlefield, its triggered ability ("When I move, draw 1") triggers and is placed on the chain.
3. State and Priority: Because a triggered ability has been added to the chain, the game state becomes CLOSED. At this point, the player who does not have focus (typically the opponent, in this scenario) gains an opportunity to respond with a [REACTION] spell.
4. The Window: Because Gust is a [REACTION] spell, your opponent can play it while the chain is in a closed state, targeting your Stellacorn Herder before the "draw 1" effect resolves.

Resolution

• If your opponent plays Gust, it is placed on top of the chain (above the "draw 1" trigger).
• The chain resolves in LIFO (Last-In, First-Out) order. Gust resolves first, returning Stellacorn Herder to your hand.
• Following the resolution of Gust, the "draw 1" trigger is next on the chain. It will resolve, but because the source of the ability (Stellacorn Herder) has left the board and moved to your hand, the effect will proceed as normal (referencing the completed move action).

Summary: You cannot react to the movement itself, but because the movement trigger must be placed on the chain to resolve, you (or your opponent) are granted a window to react to that ability before the card draw happens.