You can lay sod any time of year providing the ground is not frozen, snow covered, or mud.

However the best time for warm season grasses is in spring right after green up. Be patient and increase your success rate. Wait for spring.

If you want something green and ground cover for the fall and winter, wait a bit longer until the heat breaks and rains return, then plant some Rye grass or -Rye-Fescue mix.

I agree that you can lay it any day of the year...except this year. It would have been certain death to have laid it a few weeks ago. Now that it is cooling off, you can probably do it. Problem now is the cooling is accompanied by a very dry front moving through. The sod will be especially dry right now, so it might be hard to keep alive for a few weeks. If you can hold out I would wait until the temps drop a few more degrees into the 80s. Hopefully (for the grass) the gulf breeze will return humidity to more normal levels.

Which variety of St augustine? Avoid 'Raleigh'. Terrible drought tolerance. You live in central Texas and you may be subject to more frequent watering restriction so I would strongly suggest that you get something more drought hardy.

I think Jamur zoysia would be best all around grass.

http://www.theturfgrassgroup.com/documents/JamurZoysia.pdf

http://www.theturfgrassgroup.com/documents/williamson%20county%20-%20non-irrigated%20turf%20study.pdf

http://saturf.com/san-antonio-grass-turf.php

With La Nina coming back this winter to keep drought going somewhere in Texas, I am not sure how watering restriction would work because you need to water every day for a couple weeks plus watering restriction would even get more strict as drought gets worse.