Sorry, no. The QX60 does have carplay or android auto. You would have to upgrade the entire head unit.
Recommend you contact UNAVI, they sell an aftermarket radio head unit that may work, it has CarPlay and Android Auto for the QX60–don’t know if it is compatible with the base car radio, but you can ask. It costs ~$650.00
I installed a Unavi for my 2017 QX60 a few months ago and really enjoying it so far. It's literally an add-on to what I had so keeps all the OEM functionalities. Happy to answer any questions regarding functionality.