Ok a few things that I'd suggest...
Never max Q into W...that is such a bad idea. You max your E first and then your Q. Your wall will not have a big enough impact to max it early so it should be the last thing you max....Also if your wondering why you max your E before your Q? While your Q does more damage and is your set up skill for your pre-6 game, you need to land it (Which is possibly the hardest skill shot in the game already) and then for you to get its full damage out, need to proc it for a 2nd hit. Which isn't always an easy thing to do with all the mobility in the game. Maxing your E first will give you that huge burst potential for when you reach level 6. Once you reach level 6, you don't have to rely on landing your Q to trade since your E would do so much thanks to the chill from your Ult.
Second thing and this one is mainly a personal opinion, but I feel Athenes isn't really an amazing item on her. While the Passive and mana on kill is amazing, that's all you're really getting out of it. People who build Athenes generally also do it because they get a lot out of CDR, which Anivia doesn't really get a crazy amount out of it. Since her skills are already generally low, CDR doesn't have as much of an impact. Personally...I generally go through 2 different builds...either a pure burst style Anivia, or a more AP Tank build.
Burst AP Anivia:
Archangel Staff, Rod of Ages, Rabbadon, Zhonya, Void Staff, Sorc Shoes
AP Tank Anivia:
Archangel Staff, Rod of Ages, Rylai's Crystal Scepter, Liandries Torment, Sorc Shoes, (Situational Item: Usually between Rabbadon or GA depending if you feel you need more damage or tank).
Also her AP Scalings are amazing...I've always thought a good Anivia player is one of the most scariest champions to face in the late game.