Hi Smitha, car seat is not mandatory for Uber or taxi or any other rideshare service in New Zealand. I can guarantee you this because, I drive Uber in Christchurch. As per the NZTA exception, child restraint not required in passenger service vehicle (eg taxi, shuttle, bus, rideshare) when no appropriate child restraint is available. However, I do recommend using child seat if you do have one. There are a few pawn shops where you can get one for a cheap price. consider that option too. Also if you provide notice to taxi companies, they might bring a child car seat.