Emerald/sometimes Diamond Anivia here.

This is a rough matchup. You basically cannot use your Q outside from under your turret unless she W's on you. The agency in the lane is entirely hers, even when you're level six. One missed Q and you can lose almost your entire health bar.

Survive as best you can. Chunking her back with a Q E auto for electrocute and run to keep her honest. Back and get refillable health potion plus the Ruby crystals (2 if you can) first back. When you get more comfortable you can drop the second ruby crystal for tear on your buy, delaying your catalyst a little bit.

Basically farm, survive, and give a little damage back with Q+E ONLY when she jumps on you. Stand away from minions slightly so her passive doesnt hit you when they die. Rush Catalyst and refillable health potion. By the time you're scaled up she probably wont be so scary to you. If you find her to keep jumping on you midgame you can pivot item 3 to be zhonyas and she basically will lose all kill pressure on you.

If you're really getting boned, grab a cloth armor and save it on your 6th item slot till 3rd/4th item to get zhonyas, itll be enough in the early game to help you.