You should obtain a child travel consent letter granting you permission from the absent parent to leave the country with your child (having it notarized is not required, but highly recommended).
In the USA, though, unless there's a court order requiring permission from both parents, a child may travel (even to overseas) with either parent/guardian without showing proof of permission from the other parent.
There is no documentation requirement for domestic travel in the US for children flying with a parent. I've flown dozens of times with no one saying boo.
Can the Child (Minor) Travel Consent be notarized online? Yes. Online notarization of the Child (Minor) Travel Consent is completely legal and secure. Your documents can be notarized online in minutes through the Notarize Network, starting at $25.
Typically, minors under the age of 18 do not have to present identification for domestic U.S. travel. Airlines will accept identification from the responsible adult on behalf of the minor(s). For international travel, minors under the age of 18 must present the same travel documents as the adult.
The most important documents you'll need are a valid passport for each traveler, copies of your passport information page, proof of your address, a copy of your child's birth certificate, and any requisite visas and/or travel permits.
The US government places no restrictions or requirements on you when exiting or entering the country with your child. Many foreign governments might require require documentation for entry or international air carriers to board their plane.
Is a minor travel consent form required for domestic travel? No, a minor travel consent form is not required for domestic travel within the U.S. However, it is recommended that parents and/or legal guardians carry a notarized letter of consent when traveling with a child.