She does not need to have it for TSA or for Southwest.
If you were worried about her being your granddaughter as opposed to your own daughter you could have a letter from her parents or copy of the birth certificate if it helps you feel better, but this is not necessary for TSA.
Southwest only requires documentation for age-restricted fares for infants, child fare, and senior fare, none of these would apply to a 14 year old - she probably has a Wanna Get Away fare.
Home airport MDW, frequent visitor to MCO to see the mouse.
@DancingDavidE has it right about the official policy. If you go to Tsa.gov and look under identification, it says age 18 is the age at which identification is required.
However, if the teenager looks close in age to 18, the TSA agent may wonder, so I would recommend bringing a copy of her birth certificate. It does not actually prove anything but it might put the agent’s mind at ease. It seems like the opposite of getting “carded” at a bar, that is, instead of proving one is over age 21, one may have to prove they are under age 18. The certificate copy might save her from a more extensive search that one may get if traveling without an ID or when the name does not exactly match. No guarantees but I can see how it might be challenging for a TSA agent to guess the age when they are taught to be suspicious to protect the safety of all.