Sooo basically. You have no idea how to play against her.... or rather u dont particularly care about learning to play against her. The stun duration is short in comparison to many other abilities, The ult requires she walk up to u and is extremely visible if she's not disguised, The shield only applies after the windup is complete, therefore only when she jumps and really isn't all that big, deal your damage to her whilst she's winding up, In a 1v1 this is pretty much always possible unless ur a total melee champ because her only other CC is a root (thereby meaning you can still attack while rooted)... The best way to keep track of whether or not the champ walking up to you is really Neeko in disguise: Warding and looking at ur minimap, failing this and she ends up walking to u without u knowing, u always assume it's a Neeko charging up her ult: therefore you run or, if ur able, pop her like a balloon. The slow isn't all that noticeable tbh... but if ur really finding all that massive, you can always buy boots of swiftness (reduces the impact of slows) or buy merc boots, which reduce the duration of CC as well as giving you MR. The alternative is buying items with spellshields or cleansing effects. Itemization is a key aspect of playing in league, sometimes you have to give up some damage for more survivability... so adapt. Either way, there are items with actives that grant movespeed as well as decent Ap/AD respectively, you could always build that to help you get out of her slowfield if ur really focused on keeping the damages.
If you've played Neeko, you'll know in most cases the ult is relatively difficult to reliably land, therefore it is kinda understandable it does pretty big damage.
In terms of spotting the real Neeko when she clones, pay attention to how the model moves, if it's a continuous line with no changes, it's most liekly gonna be the clone. (this is go to rule except when near corners, at that point it's best to just guess and have another teammate keep track of one. But yh, if the model wobbles in the duration that's most likely the real Neeko. Throw a skillshot at the model if ur able, they'll generally try to dodge it if it's the real Neeko.
The E (tangle barbs) has a condition to get the empowered root: it must pass through multiple units. Easiest counterplay? Avoid prolonged moments in you minion wave or spread out in team fights.... That actively prevents her from landing the empowered E, thereby preventing her from securing all three procs of the Q.
The only real change I'd ask of Riot is to add a clearer visual indicator of when Neeko has her empowered Auto attack ready (when not disguised)