I'd try a light missile caracal in level 2 missions, if I remember correctly there are mostly smaller enemies in those missions that you'll hit better with smaller weapons. You'll be slower to kill the big ships, but a lot faster for all the small stuff.
You should also change your tank, usually you'd use something like two large shield extenders and 1-2 Adaptive Invulnerability fields, all depending on your fitting skills of course. Small shield extenders are a waste of a slot, you'll always want to oversize them: Medium Shield extender on frigates, large ones on anything bigger.
Warrior drones are the fastest ones, you might want to train Drones to V, so that you can learn Drone interfacing (+20% per level). That makes a huge difference for your drone damage, and you'll need it for the higher level missions in any case.
The Target Navigation Prediction skill also helps with hitting the small ships with missiles, and also the more expensive Guided Missile Precision skill.
Here's an example fit for a missioning Caracal, you can of course downgrade all the T2 modules if you don't have the skills to use them. You can also change the invuls to rat-specific hardeners, that should further improve your tank. Though that should not be really necessary in level 2 missions if you have halfway reasonable skills.
[Caracal, Caracal fit]
Ballistic Control System II
Ballistic Control System II
Large Shield Extender II
Large Shield Extender II
Adaptive Invulnerability Field II
Adaptive Invulnerability Field II
10MN Afterburner II
Light Missile Launcher II, Scourge Light Missile
Light Missile Launcher II, Scourge Light Missile
Light Missile Launcher II, Scourge Light Missile
Light Missile Launcher II, Scourge Light Missile
Light Missile Launcher II, Scourge Light Missile
Medium Core Defense Field Purger I
Medium Core Defense Field Purger I
Medium Core Defense Field Purger I
Warrior II x2