This is gonna be a long one, but you had multiple questions:
You said 33" tires, but how wide? I'm a very big fan of the tall and skinny 235/85-16 size, you get the benefit of increased ground clearance without any of the downsides associated with the wide contact patch most flotation tires suffer from (high rolling resistance and therefore lousy mpg, higher tendency to hydroplane when used in a light vehicle). Be aware that the load range E tires in that size are stupid-strong (you won't believe the stuff we've run over with our diesel), but they are also very stiff and in a light truck like yours would probably make you feel every bump on the road. They also don't air down too well, especially in a light truck, the sidewalls are very thick and will keep the tire from laying flat even when the air inside it doesn't. My suggestion would be to ditch whatever 33" tires you have now and switch to some nice all-terrain 235/85-16 tires, in load range D if possible.
I probably missed this piece of info, but what transmission do you have now? Dodge has never been know for the reliability of their OD automatics - if you have a stick-shift you're doing alright, if not start researching into what's involved in getting one.
As far as gears go, 3.55s should be plenty for your truck even with 32"-33" tall tires, if you had the V6 then 4.10s would possibly help reduce strain on the engine, but that 318 V8 is pretty much laughing at the tires as is. Many halfton and larger trucks were set up with that exact engine/gears/tires combo, and they are much heavier than what you're working with and they still do alright. The reality is that the main reason for your poor fuel economy is probably the engine itself - Dodge V8s tend to be gas hogs, yeah you get all sorts of good power out of them but they suck pretty hard from the fuel tank regardless of whether you work them or not. A 4.10 gear swap while more offroad-friendly will also make the engine spin faster on the interstate, so you may actually end up using more fuel to get to where you wanna play.
An engine swap to a GM 5.3 wouldn't make sense financially, you'd have to change a whole bunch of other stuff to go with that and that's most likely gonna take the kind of money that you can instead keep putting in your gas tank and still drive all over the place with your current engine and have some fun while at it. Plus you'll end up with something so custom that some repair shops won't know what to do with it should it give you trouble away from home.
Regarding axles, factory is alright for what it was designed to do - if you start pushing the truck like it's a 1-ton then yes, you'll need the 1-ton running gear to go with that. Situation gets even trickier if you regear to 4.10s - it is then that much easier for the engine to break the axle shafts. Point is, with 32" or so tires, and truck doing what it was meant to do (as opposed to attempting to climb vertical walls or pull a triple-axle equipment hauler with a dozer on it), your axles should last you fine.
So yes, if you wanna play hard then go ahead and grab a Blazer, roll the 1-ton axles under it, drop a 5.3 under the hood, doubler it, and Bob's your uncle. But she will be heavy and wide and likely tall, meaning she won't very easily fit in some place the Dakota can. May not be a concern at all, or it may be a big one, only you can make that call. But personally I think you already have a good setup for all-around exploring and general truck use. May wanna consider having a shop build you front trailer hitch, and then look into a winch on a portable mount - permanently run heavy-gauge cables to front and rear bumpers, but keep the winch at home during the week, then throw it in a tool box in the bed when you're headed out for the weekend, and drive around like it's not there at all but know that should you accidentally get in bind it may provide you with a way out. Definitely don't fall for the Mad Max cow-catcher bumpers, anything built like it's going on a 1-ton truck so it can be driven thru concrete walls is gonna be way too heavy for your Dakota - instead take a look at what the Toyota crowd are doing, they got some really nice lightweight yet strong designs, find something you like than have someone local who understands the concept build you one like that. Install a good electric air compressor with an aluminum tank - if you can stash the compressor in the cab somewhere that will be great for its longevity, shove the air tank wherever you find space for it. Use the on-board air for general purposes and also to power a front ARB locker if one is available for your truck, rear ARB is IMHO an expense that is hard to justify when factory limited slips seem to work well enough. This all should make your truck quite a bit more capable and fun to drive while still keeping it reliable and simple enough to fix.
