Hi, the bill depends on what type of gynae and ward you choose. After labour if normal delivery, by 2 days sure can discharged if no complications. For my first child, I took referral letter from polyclinic and everything was charged at subsidy rate, each checkup averaged about $50-$80 then for normal delivery + epidural about $1000 only. But I stayed in the cheapest ward and no gynae was present throughout almost entire delivery though.
If you are seeing a specific gynae now already, you can ask your gynae for an estimation of the $ you have to pay as they would know roughly from their experience.