No you dont.
Passengers under 18 do not need ID for domestic travel. You can verify this at the TSA, FAA and at your airlines website.
I travel 6 or more times a year with my dd's, as recently as late July, and I have never, ever been asked for ID for them. I have also traveled with my neices who are of a different ethnic origin and have a different last name without incident.
The exception is to verify that a child under 2 is eligible to fly for free on a parents lap.
TJ