The only tricky part is that "base plate/structure" to support it free-standing, and still allow swiveling.
The solution is something like two arms of a v sticking out to brace it up. Those two arms need to be long enough and strong enough to balance the pressure from the weight of any pot on the crane while over the fire, but also need to be spread out far enough to at least one side to brace the crane when you swing the pot off the fire.
The one other method would be a large/thick base plate. Like a 1 inch thick disk of iron that the crane is loosely riveted through. This would give you the weight to hold it in place, and then be wide enough to counterbalance the crane and pot. (Think manhole cover plate from the street!) And then have the crane stick down through it and be either loosely riveted on the other side, or loosely bolted or pinned.
Actually, an old manhole cover from the street would work pretty well. You could pin/bolt/rivet the crane through one of the holes already in it around the side. And the thickness/weight will balance out that crane in most any position. Plus, it is thick enough to not be affected much by being under the fire in the hearth.
The crane itself is a pretty normal blacksmith project. It is that base that requires ... innovation.
There are a number of old fireplace grates or fire dogs that were designed/built with a crane as part of them. The fireplace grate/log dogs provided the mass and bracing, and the crane slipped down through a pair of modified eye-bolts sticking out from the grate - so they could still swivel. (large one on top to slip the crane through, small one at bottom to slip the tenon on the bottom through)
The simplest solution would be two normal eye-bolts set into the fireplace wall. The bottom one could be just a normal one. But the top one modified so that you could open it up or with a threaded bolt/nut to connect it to the rod coming out of the wall. An adjustable top rod comes to mind. Set a threaded rod into the fireplace wall with an inch or so sticking out. Attach an eye-bolt "swivel" to the top of your crane. Then make up a section of pipe with a nut welded into each end. Be careful to get the nuts orientated right - like in a standard turnbuckle. Set the crane into the bottom swivel. Then put that "turnbuckle" on the top threaded bolts, and turn it to hold things in place. That "turnbuckle" coupler at the top could also be made from a thick bar that is drilled and threaded at each end (but with one end threaded in the reverse direction). If you do it that way, you can then really tighten it up - to firm up the whole arrangement.
Hope these humble rambling help.
Mikey - that grumpy ol' German blacksmith out in the Hinterlands