Service Dog documentation to fly, not ESA?

[Doodlebear16]

This is my first time traveling with my Sercive Dog, 16lb Chihuahua/Beagle mix, I am trying to look up needed info to travel with a Service Animal, not an Emotional Supoort Animal and all I can find is for an ESA.

What documentation is needed for a Service Animal who performs tasks for my disabilities?

Can my dog sit in my lap or on a blanket between my feet or does she have to be under the seat in front of me.  Does she need to be in a carrier at all during my travels?  Again this is mine and her first time traveling through a major airport as a service dog and handler.  I see a lot of info for ESA dogs, but nothing for other types of Service Dogs.

So what documentations do I need to have with me?

[franktravel]

Onboard

In accordance with federal safety regulations, the animal must be positioned so as not to obstruct Customers' expeditious evacuation in the unlikely event of an emergency. In addition, Customers traveling with a fully trained service animal or an emotional support animal cannot sit in an emergency exit seat. Service and emotional support animals can be placed on the aircraft floor or on the Customer’s lap (provided the animal is no larger than a child under the age of two). Southwest Airlines does not allow the animals to be placed on an aircraft seat.
Customers are not required to transport fully trained service animals or emotional support animals in pet carriers. However, if a Customer opts to carry his/her fully trained service animal or emotional support animal in a pet carrier, the carrier must be properly stowed for taxi, takeoff, and landing.