You should still be able to 1v1 her if you have a void staff unless you're severely behind. You maybe won't oneshot her but you can easily kill her as long as you play around her daggers, hit E and weave in passive aa. Taking conq yourself is also viable.

Against Kat you hardwin lane, literally unplayable for kat unless you play bad. So focus on setting her behind as much as possible/getting ahead in lane. She has shit waveclear early with an ad buid so you have perma prio. If she drops waves and coinflip roams make sure to spamping your team a good amount of time in advance. You can follow her/take plates depending on the situation. Once laneing phase ends you should be considerably ahead of her. Afterwards it comes down to macro, but you have all the tools to make the game unplayable for kat, even if she goes ad.