Here is the response I got from Joey who is a fellow Austinite and a very active member (past President) of the Austin Bonsai Society...
"Live Oaks aren't too bad to collect, they're really hardy trees if collected healthy. I'd collect in the spring before bud push (just like the rest), but I have gathered trees that were pushed over by bulldozer, trimmed them up and they've sprung to life. You must have some fine roots, but Live oaks send out very long roots and it's impossible to get a good "ball" from the wild. The plus side is that older plants don't have a tap root, and you'll find most of them have a pretty flat root base. It's the aftercare that seems to be vital. My past experience with them, is they survive collecting, but then die 6 months to a year later. Trial and error has proven two vital things (which are important really in collecting all trees, but especially oaks as they're less forgiving): well drained soil and full sun. They will need lots of water, oaks are thirsty trees, but don't like wet feet. I think your yard should do fine for them. Also, it's good not to let their roots freeze. They're best treated like Crepe Myrtle, Pomegranate and other sub-tropicals: left outside for winter rest, but set on the ground and sometimes covered. Chuck Ware has some FANTASTIC Live Oaks in his personal collection out at Jade Gardens. He's a great resource for the species!"
If you can join us next meeting, introduce your self to me, Joey, or directly to Chuck. I am sure they can help you.
I plan on starting next month but mostly Cedar Elm. I have not scouted any Live Oak source yet.