A better time might be now -

Azaleas move fairly easily and you do say yours are small, but the period of active growth immediately after bloom is not the best time for moving them. If you were to avoid just those weeks, any other time of year when the weather is not too hot would work in your zone.

Roots will be mostly surface and fine, extending as far as the widest branches. You should only find just a few deeper anchoring roots. If your weather has been dry and you are not concerned about the weight of the rootball, water well the day before. Careful not to plant any deeper than they were originally growing, mulch, keep moist...they should do well.

Thanks, you probably averted a catastrophe!

You might want to ask in the Texas forum if there is one. But if I were gardening down there, with your mild winters, I would move my plants around in the fall. Gives them the cool season to re-establish their root system.

In cold climates roots don't do much in winter, fall planting needs to be accomplished before it turns cold in order to catch the fall rooting surge.

Evergreen azaleas are very easy to move, having the same sod-like roots as other rhododendrons.

The original poster said she was in "zn 9 TX". Texas. That could be a variety of places but let's assume Houston being the northerly reaches of zn 9 in Texas. Average winter temps for Houston are 63/45F. Doesn't sound very cold to me. In fact it's only a little cooler than Scotland IN SUMMER, where, last I checked Rhododendrons and Azaleas grow (including their roots) rather well!