Nowadays private rates come with package which means you pay $xxxx comes with a few appointments and scans included rather than pay per visit which is cheaper. Delivery wise depends on gynae fee and cost of hospital stay.
Maternity insurance provide some coverages for certain pregnancy...
I got for my child medical insurance and whole life plan, education plan wise - myself had a few savings plan that i got it years back so i will use 1-2 of them for my child's education.
Lucky you mummy, Cigna is really good!