I originally started with the Faerie Charm because as Irelia early game you should spam your Bladesurge to last hit minions in your lane, and when in kills it refreshes the cooldown and your mana can dry up really fast. However I have been doing some changes as of lately and dropped the Philo Stone, and replaced Manamune and Phantom Dancer with Trinity Force and Wit's End respectively. Atmog's combo may be soon to be swapped but as of now it is still good.

EDIT: Also IMO I don't agree with the doran's items (I mean don't get me wrong they all great starting items) it's just it cost all your starting gold so there's no room for a health pot and you could buy something that could be built into something you'll use later. Just my opinion not saying your wrong and I'm right because that would be stupid this is just my mind set and how I've played since day one.

not too sure why you would start with a Faerie Charm and two health pots. Mana shouldn't be an issue as you aren't really spamming spells. You should explain why otherwise I don't agree on it. I would either start with a Doran's Shield as provides me with what I need, armour, health regen and 100 hp