If nidalee trades in battle and is saved by zhonyas, does her draw trigger take effect?

No — Nidalee, Cat Form does not draw when Zhonya's Hourglass saves her.

Her ability only triggers "when I win a combat," which she defines as remaining after combat. Zhonya's doesn't prevent her death so much as replace it — "kill this instead. Heal that unit, exhaust it, and recall it" — so when combat results are determined, Nidalee is back at base rather than at the battlefield, and she did not "remain" there. That matches the established logic in FAQ #10708 (a recalled Nidalee fails her win condition and draws nothing).

Note the unit also never actually dies in this case, so any Deathknell on her would likewise not trigger (FAQ #2596).