I enjoy playing casters more so than physical dps classes so I decided to give Annie a few games (solo queue and watched other use Annie). Compared to Ryze, Cryophoenix, and other casters, Annie seems a bit underpowered. Sure she farms really well with disintegrate, but Annie cannot really make good use for all of the gold she gets (i.e Ashe would be better with solo mid).

Here are a few problems I feel Annie suffers from:
1) Really really bad AP scaling on her abilities.
2) Molten Shield (E) is a poor ability on Annie who is very squishy. It does not really synergize very well with her role.
3) No counter for her passive makes it tedious to count (not a really big deal but it would be nice to have a counter).

Suggestions for improvement:
1) Increase the scaling of Summon: Tibbers (really should be a 0.8:1 AP:dmg ratio) and Incinerate. Disintegrate can be left alone.
2) Replace Molten Shield with some a more useful ability (damage amplification, damage link, slow, etc). Her background story refers to her as a fusion between pyromancer and warlock but all of her skills are pretty much from the pyro side. This is a chance to tap into the warlock side.
3) Add a counter for her passive.

I'm fine with the fact that Annie is squishy, but she lacks the utility and damage of the other casters (whatever she can do, other casters do better).

Hmm...on some points, i agree with you, but i dont really think she is weak. She can farm really well, with her 1st skill, and later on she will have area nuke, so getting items will be no problem..
And Molten Shield will enable her to withsand agains heroes for just long enough to do some serious damage, and also does good damage. Altogether, farmed good she is one of the deadlier heroes. But maybe some extra cast-range would be nice, especially on her incinerate ^^"

Also i like your concept of a skill from the warlock side

plus I would like to control her bear.

The only change i would like to see on annie is to have her bear not give her tower aggro when people stand in it's aoe range. At the very least have the tower aggro the bear instead of annie.

There are better nukers in the game and there are better stunners in the game.