Does Nidalee's draw trigger still work if she trades in combat

No — if Nidalee, Cat Form dies in the trade, she does not draw.

Her ability reads "When I win a combat, draw 1. (I win if I remain after combat.)" If both units die to combat damage, neither player has units present at the Determine Combat Result task, so the result is "No Result" and nobody wins the combat. Even in the odd case where another of your units survives and your side wins the combat, Nidalee isn't at the battlefield to have her trigger condition evaluated — a permanent must be present when the condition is met to trigger (Rule 383.2.c.2; same logic as FAQ #902/#1109 for Kai'sa). She only draws when she's still standing after combat, alone.