Whenever you try to q a minion (or probably anything) just as it dies, depending on the timing, the spell will occasionally go on cooldown without actually being thrown, but the spell will still display as available. So on your bar it looks like it's ready for use but you won't be able to use it until the cooldown is finished.

I'm not sure if the projectile not launching (basically akin to not bouncing off a dead target) is working as intended but the misrepresentation of cd is definitely a bug

This can happen to a lot of skills, actually. It's a miscommunication between the server (which has final say on cooldowns) and your client (which determines the cooldown to display).