I live in a similar climate, though slightly more dry being in central Texas (may move to northeast TX).
I've really liked cob. For a little while I looked at rammed earth and earth bag building, and they have their pluses. After that, light straw clay looked best. I still think light straw clay is best if airconditioning will be used in the southern US. I'm still drawn to cob though, even for a small rectangular home.
Do you plan to make the wall load bearing, or make a wooden structure to hold up the roof? I've read that only experienced cobbers should build a cob home where the thick walls hold the roof. My experience with cob was just a couple of hours in a permaculture design course.
My experience with construction in general is a little beyond that, but not tremendous. I've been a carpenter's helper and a pipe fitter, then I built a 180 sq. ft. tiny barn apartment that I'm still working on, part time, 1.5 yrs after starting. I'm just on paint and trim now, but I hate conventional wall coverings, flooring, and trim. I enjoyed the framing though.
The next home I build will be stick frame, but the studs will be 24" on center, and there will be a single top plate since the rafters will connect to the top plate right above each stud. This meets building code (if that matters for anyone else) and is called optimum value framing.
I'd consider cobbing around that type of framing. The ceiling joist would then be 24" on center too and that's great for attaching the ceiling material of choice.
A thick earthen, cement, tile, or stone floor should help cool your home. Place a window high up on the wall to exhaust heat. Find out where the summer breeze flows from. Place water tanks or ponds on that side of your structure. Plant lots of plants. Shade the home with vines on trellises if the trees grow slow, or there's no room for trees. Use porches or big overhangs and consider a dog trot floor plan, so the wind will speed slightly between the two little portions of the house connected by the roof.
Yes, I do believe people can build without taking these courses. Don't be afraid to make mistakes and build a smaller less important cob item first, maybe a fence portion.
There is a ton of info / images of 2x4 framing online, and many people you know will know at least a little bit.
Of course, hunt for used wood, but 2x4's are worth it.
An alternative to stick framing would be pole barn type framing, but ceiling joists would be separate from the fewer rafters, then perlins would connect each rafter beneath the sheating. I don't know if pole barn construction would save $ or materials, unless you have/ can find sizable round posts.
Timber frame is more costly, especially when paying retail for the timbers.
Still, strongly consider framing this earthen structure.
Edit: I realized after writing that you are probably very attracted to the round organic shaped home. Building without a wood frame would definitely save you money and fits that wall shape. Do you have time to practice cobbing? Maybe you can learn on your own to build well enough to make it load baring. I don't think you're in an earthquake zone. Also, putting a light roof (not soil ) should lessen the load that the walls will carry.