How the hell do you counter Diana
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Same way you counter 
You don't.
Dodge Q. Step away when moonsilver is up. Stun her as she dashes or right after.
And if you were going to write "she just kills me with R-Q-E without passive" - uninstall.
She's so horribly feast or famine it hurts, I hope she gets reworked into a proper AP fighter at some point. As for countering all that really comes to mind is heavy petting poking.
Play Cho'Gath. Nom nom nom nom nom nom.
She needs to hit all of her abilities to kill you unless she is crazy fed. If you dodge her Q or go in when it is on cooldown, then you can kill her