How can I put a dog door in a nine panel glass exterior door?

No.

Depends...If it's tempered glass absolutely not. If it's not then it depends on whether or not your dog will fit through a doggy door the size of one of those nine panels because that is the only way you can possibly make it work. Even then I'd have it professionally done because you're asking for issues doing that to a glass door.

Depending on the quality of the glass, yes.

https://www.doorglass4pets.com/

https://www.petdoors.com/pet-doors/pet-doors-for-glass.html

https://www.petdoors.com/pet-door-guys-in-the-glass.html

I wouldn’t recommend it. Any thief seeing a panel or pane missing from the door would recognize either an entrance to your house, or a place where a lock might be accessed to enter your house without breaking a window. If you do remove glass to build a doggie door, I suggest that you make the door of plexiglass so perhaps the missing pane is not visible from the street. Let’s see what others say. ☺️

This one is in the back of the house and there is a high privacy fence and not visible. I do worry about security and your comment is very considerate and thoughtful...thank you so much!

I like the idea of using plexiglass. You could make "hinges" with loops of wire attached to tiny eye hooks.

My concern is the manner in how your pup will use this door? Is she a dainty lady or will she burst through it like a little hellhound? If pup's aim is off she may go through the wrong pane.