I like pp questions. I think you should also ask the doula what her philosophies/pov is. Some doulas are very natural birth oriented and may not be supportive of different choices or vice versa. So you want to ask questions that show you guys are a good match.
People hire doulas for different reasons, some because they want to avoid pain meds, some because they want general support for the birth process or have a partner who has issues and cant provide support, etc. The first step for you should be to ask yourself, "why do I want a doula?" Then you can ask the prospective doula questions to see if she will fit your needs.