Thank you all for your wonderful information and advice. I called the NTTG (thank you for the links) and they told me I had 2 options.
1. To open an Zip account with $40 in it, and then to close it after our visit and we would eventually get any unused money refunded.
2. Do it through Avis. I called Avis, then Avis at DFW. They told me that all the cars at DFW have TollTags, and they will charge us $2.95 per day plus any tolls. Obviously, this will be charged to my credit card when they get the info from NTTG.
We're going to go with option 2. I'll report back if we have any difficulties.
I'm not quite sure how the construction is going to impact us - we'll just have to hope for the best and hope the GPS can get us around the worst of it.
Thank you, everyone.