Hey Jules
I had a doula for my attempted induction and ultimate emergency caesar 18 months ago at a Melbourne Private hospital.
She enhanced the experience enormously for us and advocated strongly for us along the way. She was very supportive having worked tirelessly with us in the lead up to the birth. I have such great memories of the birth even though it was nothing liked I had hoped due to all of her hard work.
I had to advocate VERY strongly for her presence in delivery in the event of caesar but got her there in the end (admittedly I have previously had a couple of very hairy hospital emergency experiences which resulted in some ptsd which probably was a persuasive thing for the hospital allowing her to come in).
Happy to give you details about her and the whole thing if you want to PM me.
I hear Sam Hargreaves is excellent and very open to these things too.
Cheerio and good luck
Belinda.