Late Flight Transportation

I'm planning to fly into Queenstown kinda late (landing at 9:20pm) and the rental car place will be closed. I've never had to get a taxi or Uber from the airport in NZ. My planned hotel doesn't have a shuttle. My plan was to get a ride to the hotel just to crash and then go back to the airport in the morning to get my rental car. Will an Uber pick up that late or am I better off getting a taxi or different hotel that has a shuttle?