That was my first guess but the air train is not a single seat ride which everyone complained about when it was first built. You either take it to Jamaica Station and catch the LIRR or J/Z train or to the Howard Beach/JFK A train station.
I love public transit and opt for it if I can, even if it's a bit less convenient. Only remember a few cases where Uber was the best choice, definitely Las Vegas was one of them but if I can I'll never return there anyway.