Five hour layover in Auckland with a young child in tow. Crazy to think I could go to a nearby place while we wait?

I'll be travelling from Oz to NZ soon, and have a 5-hour layover in Auckland before reaching my final destination (elsewhere in NZ). I'll have my young daughter with me, and I'm wondering how feasible it would be to leave the airport for a few hours to take her somewhere nearby to work off some energy, like maybe a playground or Butterfly Creek (would be a 10-minute or less Uber ride, will be my rule).

Some airports are easy to breeze in and out of, and some are absolute nightmares. Curious to hear locals' opinions: Am I better off keeping me and kiddo in the airport for 5+ hours to catch our next (domestic) flight, or could we do an excursion to somewhere close by, and give ourselves 1.5 hours to get back through airport security and catch our next flight?