Johnny,

Generally speaking, the rut in south Texas is during late December – give or take.  There are many ranches that intensively manage whitetails in Duval County, so the herd densities, nutrition levels, etc., can be significantly different from ranch to ranch.  All these factors can impact the timing of the rut on a site-specific basis.

Talk to the folks that manage the property where you hunt for a more specific answer.

Growing Deer together,

Grant