That's a good picture, when it's magnified it shows a lot of details that are invisible to the naked eye.
Sorry to tell you this, and I hope I am wrong, but I think from its appearance that your little chinquapin may have what is called Bur Oak Blight (chinquapin is related to and cross-breedable with bur oak and is susceptible to some of the same diseases). Those miniscule white dots along the capillaries are not leaf texture, they would be the suppurating pustules that are precursors to the browning, blackening and curling that starts on the leaf margins then spreads inwards to the center. Bur Oak Blight first presents on new spring foliage in late spring to early summer and progresses through to autumn before going semi-dormant in winter. There apparently are some treatments that can be tried.
I don't know what else to tell you other than the above since I'm not familiar with the many types of oaks that grow south of the 49th parallel that are tolerant of climate conditions and the types of oak diseases that present in the south. You need to do some research about Bur Oak Blight - if possible also maybe take a leaf example (one that has lots of those white spots as well as the black curling on it) to a tree nursery for confirmation about what the problem is.
If the tree is treatable, that's good, but if it doesn't survive and you decide to try again with another dwarf chinquapin I'll suggest you do not plant a new one in the same location. Also don't wait until autumn to plant a new one, get a new one as early in spring as possible so that it has the whole year ahead to become very well established and more immune before the following winter sets in.
Here is some good information about Bur Oak Blight that may be helpful in determining if that is what your tree has:
https://hortnews.extension.iastate.edu/bur-oak-blight
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