As Duality said above, support skills are damn important if you want your ship to perform as well (or close-ish) as those mean players from 2003 can make it perform. For your domi, tech 2 heavy/sentry drones (Ogre II, Garde II etc.) will make a huge difference to your damage output.
Your armor skills can also be boosted by training the various compensation skills (Thermic Armor Compensation, Explosive etc.). These will improve the armor resistance bonuses you get from EANMs and other passive hardeners, making your tank and effective HP better.
For engineering skills, you can get Energy Systems Operation to 5 and Energy Management to 4 within about a week, which will help your cap recharge rate a lot, maybe freeing up a low or mid slot for something other than cap rechargers/power relays. Energy Grid Upgrades can be trained to level 4 as well, letting you use the very useful Power Diagnostic System II mod.
If you're going to be flying other Gallente ships, you'll also want to worry about gunnery skills, since a lot of gallente ships get their primary damage from blasters/railguns. Controlled Bursts, Sharpshooter, Rapid Firing, Motion Prediction and Surgical Strike are all very useful, and training them all to 3 or 4 wont be a huge time investment.
(You appear to have made the same mistake as me, and have trained for a battleship without being able to use battleship turrets. You should probably fix that soon unless you only use drones when you fly a BS)