Well, assuming BIGTEX is in Texas, none of the spring majors have an age limit (mouth rule), I don't know about Dallas though. I do also know that there are alot of county shows in TX at all kinds of different times of the year and that some of them have very specific age and/or weight limits, so I'd contact your CEA or VAT about local and/or county rules.
I think that the age of the steers most commonly shown has alot to do with the time of year they're being shown. Down here where we target late January through early March shows, and alot of people calve mid July - September, those are primarily the age cattle we feed for those shows. The same goes for our October state fairs and March - April kind of calves. As you go further toward the midwest, the state fairs get earlier, but the March - April calves are still most common, and they're still what most folks feed, even though their target date is earlier than ours is with calves born at the same time. Prob'ly also has something to do with the fact that most cattle simply won't gain quite as well during the hotter summer months down here as they will further north.
As Malinda said, there's alot of difference in getting a butcher calf ready to eat and feeding out a show steer. The cattle we're showing down here are capable of reaching market weight at a younger age, but one much less than 18 months rarely has the maturity and mass to be a serious competitor, so we bring them along a little slower and try to hit our target weight at a later age.