Ask Mr. Smarty Plants

 I suspect that Mr Smarty Plants took long enough to get to your question that perhaps they are not flowering anymore.  If so, you are good to go!  Several websites indicated that pretty much after they flower, through August, is OK for digging them up and transplanting them.  Here is a webpage by the Univ. of Illinois Extension and here is a similar take from the North Dakota State University Extension.

     You should have concern for the success of your transplant though.   Like many native plants, the Iris spp. is sensitive to its surroundings and if you are moving well away from the Texas climate it is adapted to, then it may not do as well as it does here. If you are moving far, you may want to consider leaving these ones where they are and getting a new native Iris that is adapted to your new home.

  There are 26 different species of native Irises. You can see the list of these by going to our Plant Database and searching on “Iris”.  Over a third of these are native to the West Coast.  Iris brevicaulis (Zigzag iris) is native to a few counties in Texas and several Central States stretching to Canada!   Another, Iris hexagona (Dixie iris) is native to several counties in Texas and [like the name!] most of the Southern states.

         
Iris hexagona                              Iris brevicaulis

Good Luck with your move!