The answer to the above question is, no, Austin is not prone to many Natural Disasters. The primary force of nature which Austin is hit with is tornadoes. Second to that would be flooding, however there has been a drought for approximately two years – thus eliminating that from the current Natural Disaster scenario.
One can view the breakdown of the Natural Disaster records for the Austin area here: http://www.usa.com/austin-tx-natural-disasters-extremes.htm
Overall, this makes Austin a pretty safe place to live if one has a concern about Natural Disasters.