According to NOAA, March 14 is the average date of the last spring freeze at DFW.

The following information is by TAMU, so you should wait until the temperature stays above 40 degrees.

1. Q. Can broccoli be grown in the spring and the fall?

A. Generally, yes, depending upon the variety, the area of Texas and the time planted. Broccoli does best when temperatures remain between 40 degrees and 70 degrees F. during the growing period. In most areas broccoli grows best if planted in late summer so it can mature during cool periods. Temperatures below 25 degrees F. can damage or kill broccoli. Broccoli should be planted early enough to mature before these conditions occur.

I would go ahead and put it out. You may want to harden it off a little first though(put it outside for longer periods each day so it can acclamate to the sun, wind, and cooler temps.
Broccoli and other cool weather crops can stand pretty cold temps. Since broccoli takes a while to mature it's best to grow it as a fall/winter crop in our climate. My broccoli matured and was picked in early January. Temps fell into the 20's a couple times and it still survived.

Pete

You can put it out now. Mine is out and doing great for the last two weeks.

Sorry ltcollins1949, but you didn't quite read that carefully... The TAMU info does not say to wait until it is over 40 degrees, it says it(grows)does BEST between 40 and 70 but that anything below 25 will kill it. We RARELY get below 25 here in my part of Texas(DFW). If you wait too long the temperatures will get too hot and the broccoli will bolt and flower. I have a little straw mulch around mine and it keeps it nice and cozy when the temps got down close to freezing.

Get yours in the ground now and start looking for your cream of broccoli soup recipe!

Here is a link that might be useful: Deirdre's Garden Diary

Thanks for the helpful advice; however, it looks as if my young broccoli has fallen victim to my dogs during the transition to the outdoors. I'll try again in the fall!

Do try again in the Fall! I tried Broccoli last spring and it was a miserable failure. Once the temps hit 80*, it tries really hard to flower.
I bought plants last fall and put them in the ground in November. They took several nights well below freezing and just bounced right back. When we harvested this month the flavor was amazing! We really could taste the difference between ours and grocery store broc.