I guess that you will need to look at some campers and decide on the model that you want to buy. Then check the weight of the camper.
You mention living in it full time for a year. That means that you will need to take everything you will want with you for a year. That can mean 1,000 pounds of cargo in the truck, things like bicycles, clothes, cooking stuff, food for a week or so. Are you going to get a generator so that you can dry camp or run solar panels so you can dry camp silently? If you are moving around every 2-3 days, then the alternator will keep the battery full, but if you will be parking for a week at a time, then 200 watts of solar panels will help out, you will not need more than 1 battery (keeping weight down) and still have plenty of power to use in the daytime, with a full battery every night for use then.
SunElec.com had a 140 watt 12 volt panel on sale with a frame for only $229 a few weeks back. Add a 20 amp PWM controller, a couple of brackets, and some wire from Home Depot, you will have a decent solar system. The RV will consume 35 AH daily just to run the CO detector, propane leak detector, and refrigerator. This is about what one of my 120 watt solar panels will collect in 1 day.
As for extra tire cost, the skinny dually tires are a little less expensive to purchase, but will last many more miles as they carry less weight per tire. Usually the tire cost is not a issue with a dually owner. It has more to do with weight capacity.
Say you find a perfectly good camper layout and the overall weight is only 2,200 pounds. It probably will not have a refrigerator though. A SRW 3500 probably has 3,000 pounds of cargo rating, and will carry it, you and your stuff.
But a slightly larger camper with a refrigerator might be in the 2,500 or 2,700 pound range. How much water will you carry? That makes a huge difference too. I carry 100 gallons of fresh water in my 97 Bounder, and can dry camp 3 weeks at a time, taking daily showers. I save a huge amount on camping fees because I have 400 watts of solar power, and can watch TV with my direct TV antenna all day and night if I wanted to. Then spend 1 night in a campground where I can dump, recharge, and fill that fresh water tank again (800 pounds).
No I did not get 'great' mileage. I would get 7 MPG at 65 MPH, or 8 MPG once I switched to 91 octane, and slowed down to 55 MPH.
If you plan on living in it a year, you might also consider a smaller class C motorhome. They will have a full size shower, bed, larger refrigerator, and normally will come with a generator. This will all make living in it much more comfortable.
Check with your insurance agent. Insurance on a RV is probably pretty cheap, as they 'expect' them to not have many miles per year, and overall are pretty low cost as far as accidents are concerned. If you will be staying parked for a long time, say in a RV park for 4-6 weeks, you can also call the agent, tell them to stop the liability part of the insurance until you are traveling again.
So back to the truck. in 2004, the F-350 dually had about 12,000 GVWR, and could carry around 4,000 pounds. The 2004 F-350 was 9,900 GVWR, and could carry only about 1,500 pounds in a 4X4 diesel crewcab version, as the base curb weight was well over 7,800 pounds! In 2005, that improved a LOT. Ford went to 18" rims for the SRW and 17" for the dually, with much larger brakes. Now it is 14,000 pounds GVWR for the dually, and 11,500 for the diesel crewcab SRW. So you can carry around 4,000 pounds in a SRW after 2005. However I would not recommend the 2005 - 2010 Ford diesel to anyone. The V10 made lots of power, but mileage was not all that great, perhaps 10 MPG. And the gas version was much lighter curb weight.
So check the GVWR of the trucks that you are looking at. Check the curb weight too. This is the main factor that will decide dually or not. If you have a F-450 pickup, it will carry any camper that you desire, and still have the ability to tow another trailer with a 1,000 pound hitch weight. If you select a SRW with 3,800 pounds cargo rating, and decide that you want to tow a horse trailer, you might need to upgrade! But if you keep it light, you should be fine with just a camper and all your stuff inside.
Good luck,
Fred.