The fighter whose carrier is destroyed is “stranded”. At the beginning of the noncombat move phase, before the player whose turn it is makes any movements, fighters whose carriers have been destroyed from under them or who scrambled from an airbase whose territory was captured during the combat move phase can move one space to find a landing spot (either an adjacent territory, an island in the sea zone, or a carrier in an adjoining sea zone). If they cannot find a landing spot, they are destroyed.
In your situation, the landing won’t happen until after the battle in the territory where you want to land has been decided. The plane’s eventual survival depends on the outcome of the battle, but it does not take part because it is still in its original sea zone.
Hope this helps.