That's about how much it costs (after insurance) to give birth in a private hospital in Australia as well. This is in a country that has universal healthcare. The largest costs are the often the hospital fees.
That doesn't match my experience. We have private insurance while on 457 and the only out of pocket expenses were the genetic extra test for autism and sex of the child and me staying couple nights in the hospital with my wife. About 750 in total. Everything else, pregnancy handling, hospital, midwives, cesarean, anesthetics were covered by the insurance company totaling around 20 000 AUD.
If you go through the public hospital system (aka universal healthcare) the cost is negligible. Around 70% of people choose the public option.