his high damage isn't due to his attack power bro. It's the fact that he has 3 spells that do aoe dmg that have short cooldowns. He has BURST damage, due to Q + R + E combo (and W if no one's around and you don't need the escape).
trinity force is great on him, as it allows him to slow, which allows targets to stay in range of his rockets. Added mobility and crit chance due to zeal? Extra damage, and extra mobility.
He can solo most champions because he does so much damage with Q. When you get rockets? Oh man. To quote a teemo I went up against (who gave me a hard time cuz he was good). "Man Corki is OP"... "give me a long range short cd skill that does high damage".
as for his squishiness, yes he is VERY squishy. Having a champion do as much damage and making him durable would be unbalanced. To compensate, you have to use your range and mobility to stay out of range out of disables (knowledge of enemy champ's skills and summ spells are key here). You may not be hittable, but your rockets sure can. If you ever do find yourself in a bind, you can valkyrie away. It's his escapability that allows him to survive, just like Kassadin, Shaco, and Nidalee all have escape moves. They're all squishy but notorious for being hard to kill. Also, if you do get CC'ed in some way, take cleanse. Cleanse + flash and you should be pretty hard to kill.
also, guides will only point you in the right direction. I've read a ton of guides and thought my item build was to blame for my bad game but when I see a nasus or a corki or _____ champion own hard with just a sheen or doran's shield or _____ I realize it's all about smart play.
and with corki you have to be on your toes. His low hp does not give you room for error.
watch MrGrimm's replay against a teemo. He does well. And you know... I HATE laning against teemos.