I think that young-earth creationists—the evolutionary ones in the closet, anyway—would say that God created the original deer "kind" (is that even defined yet?), preserved through the global flood of Noah, which evolved through mutation and natural selection into all the historical and current deer species. [1] That original deer "kind" is probably long extinct and no one knows what it looked like.
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Footnotes:
Georgia Purdom and Bodie Hodge, "What Are 'Kinds' in Genesis?" Ken Ham (ed.), New Answers Book 3 (Green Forest, AR: Master Books, 2011), pp. 39–48.