I don't personally fly Gallente, however I do fly in 0.0 and a fellow Corpy (who is Gallente) uses Brutix's and Ishtar's for PVE.

As you have specified going for drones, then the brutix is out its a blaster fit I know for nearly 1000 DPS versus Guristas, and for cheapness the Ishtar is definately out.

Domi would be my first choice of the two you have selected, but your problems will be speed and maneouverability related rather than damage.

First I would always carry Warrior II's to handle warp scramming frigs as a matter of priority. Then let the Domi tank while you set sentry drones to work on the Rats. I would also keep a flight of Hornet ECM drones if possible and the second you see Probes on directional scan, deploy them, break lock and cloak up.

No matter what ship always have a cloak fitted, and when in doubt always be pre align to a celestial object to fix your maneuverability issues (But not a Moon, as there will likely be POS's with Neuts, webs and scrams there to great you!!!!!)

There is still a chance that you will land in a signiture that is being camped by cloaked PVP pilots waiting for hapless PVE fit ships to come in, however I've never had this happen to me personally, probably because I run with a group of us and safety in numbers.

That said in reality you are probably at your safest when you are in the signitures, it's getting to and from the stations and target systems that are the hard part.

Other things you can do is research the rats in the target region and train up the racial drones that deal their damage weakness, also fitting hardners to the damage that they deal out etc, I'm sure your aware of that from your hi-sec adventures. :D

Seperate out Local channel and watch it like a hawk, information is life and will save your backside, always run away if in doubt and come back later.

Watch out for Bubbling Gate camps, or Hictors and Dictors, they will ruin your day no matter what ship you are in, and respect your surroundings and highten your senses. Everyone wants you dead and the second you forget that you will make a mistake and get caught. If you have never been in 0.0 the first time you see a bubble you almost certainly will scream like a little girl and wet your pants, (Speaking from experience, well maybe not litteraly but you get the idea)

Have an exploration frig to probe out your sigs, I know it's another ship, but small frigs have a higher survivability then moving around in a battleship.

Watch for the same bubble camps at a station... Large tech 2 bubbles have a range of 40KM!!!!! if you drop out of warp 40KM from a gate or station in a camp even in a battleship and a MWD you will be dead before you get to 20KM from the station. So create insta warps and 200+KM safe spots around the gate to scope them out rather than going direct.

Also its a good habit when traveling to systems to not go gate to gate in 0.0 going to a planet off the line of a stargate warp and going back can help you avoid said bubbles.

Lastly never fly what you can't afford to loose, I've have such a ball in 0.0 however it is completely cut throat, and no matter how good you are, you will loose stuff in here. If you are coming in to make money, be aware and always have a back up ship in reserve and budget for a number of losses. If you are here for fun you will find it along with frustration and anger :)

You will get a lot more mileage if you can get in a local corp or alliance so you have some protection or back up if it goes wrong, but this isn't always possible and may impose certain limitations on what you can do that may be impractical or unacceptable for you, but put it like this, say there are 4 major alliances in your chosen area of space if you are aligned with one of them thats only 2 or 3 that will shoot you on sight rather than 4 and I prefer those odds personally, they may even come to your rescue if you do get attacked.