There is no law in Texas that states a specific age at which children are automatically qualified to stay at home without a babysitter. The Texas Department of Family and Protective Services (AKA CPS) has provided on their website that many factors need to be considered before leavings your child unsupervised.
Adequate supervision is critical to keeping kids safe. An adult caregiver is accountable for the child's care and inadequate supervision can be a type of neglect (neglectful supervision). Here are some of things you should think about when deciding how closely to supervise a child:
• How old, emotional mature, and capable is your child?
• What is the layout and safety of the home, play area, or other setting?
• What are the hazards and risks in the neighborhood?
• What is your child's ability to respond to illness, fire, weather, or other types of emergencies?
• Does your child have a mental, physical, or medical disability?
• How many children are being left unsupervised?
• Do they know where you are?
• Can they contact you or other responsible adults?
• How long and how often is the child (or children) left alone?
See: Tex. Dept. Fam. Protective Srvcs - FAQs
The best advice is, if you have to wonder then better safe than sorry. Keep the babysitter/daycare on the payroll for another year and take comfort in the piece of mind you get knowing your child(ren) is/are safe.