Don't overlook small, dead trees, either still standing with the bark falling off, or fallen ones that are up off the ground. It takes a little longer to gather a pile of, than if you're splitting big rounds, but that small stuff will in most cases be dry enough to burn immediately.
A friend recently moved into a new-to-him house and got a stove a couple months back, and I've been sending carloads of it back home with him every week, until he can build up his stock of dry wood. I told him to contact a tree guy who will drop soft Maple at his place..that stuff will dry in a year. Once he's a couple years ahead on his supply, he can start adding Oak or other longer-burning woods that need more time to dry.
Quercus cerris AKA Turkey Oak. ("Turkey Oak" in my Audubon Guide, North America, is a different species, though..??)
The rounded lobes of the leaves of your specie would point to this being in the White Oak group...if so, I'd think it should have high BTU output, almost equal to that of Hickory. Have you burned it? Does it burn long? If it grows well there, and fast as you say, I would spread more acorn from that around and get more of them growing.