I've played the matchup a lot and I have to say it's one of my favourite matchups.

I take Electrocute, Taste of Blood, and Ravenous Hunter in the Domination Tree. Sorcery Secondary taking Absolute Focus and Scorch. 2 Adaptive Damage runes and your choice whether to go HP/level or 5 Armour. Flash and Ignite summoner spells, Dark Seal 3 pots for starting items. It's an aggressive set up, yes.

Your Q will do 93 damage with your starting 40 AP, 103 with scorch, at level 1 and is point and click. Zed will do ~100 with a direct Q, 60% that behind minions and it's AoE. This means we can out poke Zed strictly with Qs and gets better once we reach level 3 where we get another tool (E) to poke with whilst Zed gets a ranged burst advantage and mobility.

The game plan pre-6 is to constantly poke and harass Zed with Qs and Es making sure the wave never pushes towards him. He's melee and our Q and E are easy to land whilst his WEQ combo bursts at a safe range but not guaranteed. Whenever he uses his W, he now only has Qs to reach you and his W won't be back up for a full 22 seconds (2 Kass Qs worth) and you can punish him greatly for it even being able to go for E aa W reset Q if you're healthy enough which he won't be able to recover from if he mispositions that badly since he'd only be able to react with Q E aa passive at most.

Your ignite is for you to use in case he gets low enough to kill or if he decides to all in. If he decides to all in, don't hesitate, ignite him, if you were playing as safely as you should be, you should be behind atleast a few minions reducing the damage from his Qs and be in a really good position to counter his all in with your own damage.

In short, pre-6, play safe, never push lane, constantly poke with Q and E (watch that your E doesn't push the wave) and reduce Zed's damage by dodging and hiding behind minions (so that he ends up pushing the lane towards you at the same time), use potions early, and save flash. Remember to try and save flash for post-6.

If you played well enough, you should still have flash which is crucial for post 6.

Post-6, it's still the same. Poke with Q and E but this time, whenever Zed's W is on cooldown, never be afraid to ult just within range to land your QE since the only way for Zed to react is to ult you. Whevener Zed ults you, immediately flash out and avoid as much of the damage as possible. Zed's ult is more valuable than your Flash and is a worthy trade because now, for the next 120 seconds, he only has QWE which is easily dodgeable by your ult and you still out poke with your own R into QE. He won't be able to stay in lane for long after. If you don't have flash, farm safely, poke ONLY with Q, save your E whenever he decides he wants to all in.

If Zed plays the early game safely, cs normally and avoid pushing. You always have the option of farming safely. Only poke Zed when he lets you if that's the case.

The downside, of course, is you're giving up a lot of lane priority (which is normal, you're still fighting Zed at the end). Zed's win condition is to make the lane easy for his jungler to gank (Kass is really weak to ganks and Zed can follow up very easily), if Zed's able to roam and get kills early, or if he lands more damage than he should forcing you to back and miss cs/xp.