push in the wave against her. it pressures her to use her q to cs instead of being able to use it to poke at you.
since you dont have alot of kill pressure on her, you want to do this anyway. push in the lane as fast as possible, then roam mid, or tp bot or use the time to get scuttles or some vision into the enemy jungle while it bounces back.
youre not really trying to fight her, because its pointless. you just want to shove in waves against her and then use the next 30 seconds as efficiently as possible to get some work done somewhere else on the map. even if its just setting up vision and confirming where the enemy jungler is, for your team.
be careful to stay away from walls. your best bet is to rush armor and health early on. if you see her activate her w to get into position for a wall slam, have your own w ready to absorb the damage in case you cant prevent it.
shes probably one of the few matchups id recommend the meme build into. you go cinder + chain vest first to match her waveclear and then into cleaver, since shes going to rush sunfire aswell. early ninja tabi help a lot with her shield poke.
the only thing that anoys me really about poppy is how her shield lands next to a wall 80% to 90% of the time when she throws it at you, which means you cant contest it, which menas she gets it for free, or you get slammed into the wall trying to destroy it and she gets free damage on you. kindof defeats the entire purpose of the shield drop as a counterplay mechanic, but whatever.
dont go for her shield if youre not certain you can get it for free.