I expect to give birth in less than a week, בשעה טובה. It is very important to me that the doula be with me for as much time as possible- I hired her to be there to keep me calm and if, by chance, there is a Kohen warning outside of the hospital at the time when I need to go in. My husband is a Kohen.
I have hired a doula who said that she will answer her phone on Shabbat/Yom Tov. The question is can we call her and, if so, at what point can we call and how often.
When it is clear that labor has begun or is imminent, you may call the doula to assist you and accompany you to the birth.
See Shulchan Aruch 330:1-2 and Mishna Brura ibid.