As is typical at the start of the expansion the fairy is nerfed to near worthless, and she won't improve until your gear does (pets scale well with ilvl, so they nerf embrace at the start of every expansion).

Your dungeon role early on is simple. Since it's early and few have decent gear, take note of the size of the pull. If you don't know the tank, then if there are five enemies or more play conservatively, especially if there's more in which case you might need to spam heals. Excog the tank, and use Art of War until Excog goes off. If the tank isn't dropping like a sack of wet paper, then use lustrate + whispering dawn while continuing to Art of War. Use Lucid Dreaming when your MP hits half. Feel free to adlo the tank if you want a breather, and don't be afraid to use recitation-adlo when you get it. You can also hit each target with biolysis if you want, which can help conserve mana.

If at any point in time it looks like your tank is taking too much damage, then adlo and physick as the situation requires. If your party members are also goofballs who stand in fire, then save a stack for indom. Feel free to Art of War while you have aetherize charges and excog/lustrate while spamming, but if you're out of charges don't be afraid to throw some adlos. Also use Fey Union on large pulls, but make sure you support heal, as it's too weak currently to leave it to the fairy unless you and your tank are geared.