To quote Illaoi:
: "Move!"
Literally the entire counter to her kit is to walk out of range. If you stand there and let her pummel you to death, you will get pummeled. To death. It's like standing on train tracks and saying it's the train's fault for killing you, when you could have walked three feet to either side and been totally fine.
Dodge her E, and she's got nothing in a 1v1. You can sidestep her E and her Q, her W is basically an autoattack, and her tentacle zone from R doesn't go anywhere. Buy
and
, and congrats, you've countered Illaoi.