Okay, just to cause you a little more trouble...
https://www.realwagonwheels.com/
You could probably frame it out with either 2x4 or 1x6... Make chuck wagon style panels out of half inch wood slats & 1x2 posts. Attach the hoops to the frame along with the axles. Truth is if you know the diameter needed for the axle, again a pipe welded to a plat can do the job. I'm Leary of 1/4" plywood as it tends to warp really bad, but maybe some combination of 1/4" and 1/2" to make the actual coop & nest boxes. I'd probably just go with half inch for that. Just thinking out loud here. Half the fun in a wood working project is the design phase.