Just recently bought Annie after playing with her once when she was on F2P, and while she starts out slow, she is a complete DPS MASTER after you get Tedder. Past level 6, just go for minions near a turret until an enemy champion is stupid enough to get near you, and unleash the bear. Tedder has insane DPS and can tear down turrets and champions in a single summon, and the fact he has a fast ability reset speed makes her even better. Annie can stand up to the best of champions, just get a bit extra armor and health, don't worry about offensive gear, let Tedder do the work for you