her E has a 14 CD at max rank, the refund requires it putting a champion asleep. her q has a 4.8s CD at max rank.
her q's damage is reduced by making it travel less, reach move or dash and beat the tartarus out of her. rules of trading not violated.
the biggest problem while trading properly with her is her built in lich bane without a hard CD that her q can double proc.
her full combo of .... after attempting to right the 2 different ways her full combo can be done and what is usually considered her full combo is done i realize most zoe's don't AA enough(like half of the passive empowered AAs aren't thrown(attempt an AP bruiser build and see if damage has a significant enough fall off with getting in those extra AA??)) and it takes far too much space is mostly so powerful as the current state of ADCs make it very difficult to justify building MR as anyone but her laner or in the rare event of the enemy stacking AP champs.
her unsuccessful e combo of q(summon), AA, q(throw), AA, w, AA, with an ulti and AA somewhere between is significantly less damage.
the actual q(throw) is variable as it is dodgeable.
the point is when she misses her E she is easily punished. she barely broke positive WR in NA plat+ play during 8.2 for a reason.
furthermore

all of these items are good against her, that last one is amazing against her
TLDR; Just because you haven't figured out how to trade against her doesn't mean she can't be traded against.