You need to be aware that there is very little room to manoevre during a c-section. After DH (holding one hand), 2 surgeons and a nurse (working on getting bub out) and an anaesthetist (working with my other hand) and the midwife and paed waiting to look after bub - I don't know where I would have put another support person!
If the point of having your Doula is more to support from a distance you could probably negotiate that she is in theatre - but it would be physically tricky for her to be within a metre of you.