My kids are older, so things may have changed since they were this age, but most of the organized sports didn't start until age 4 or 5. My older son was asking to play soccer at age 3 and he was too young for a team, so I signed him up for a class at the Rec Center (in Garland they have several awesome Recreation Centers that offer all kinds of classes at a great price, probably have these in Oak Cliff also.)
Is your daughter very athletic/coordinated? Does she like to kick the ball around in the backyard? My son was not really very athletic and did not handle the competition well. He could not stand to lose! Even though in early sports they supposedly don't keep score, but the kids all know which team won! I realized that he really didn't want to play soccer, he just wanted the uniform! Bought him a soccer jersey and shorts and he was happy! Ended up never playing on a team.
The YMCAs are also good. They have all kinds of sports teams, just not sure the age limit, but I think there were a couple of 3 year olds on one of our T-ball teams. What worked best for my younger son (who is also not very athletic) was to play on Upward teams. This is a program that is usually sponsored by a church. It is not as competitive and puts more emphasis on sportsmanship and learning the game. You are less likely to have ugly, overly competitive parents!
So, I would consider your daughter's temperament, maturity and athletic ability. Most kids do start sports pretty young, but not all kids are able to handle it.