Cab is about 20 minutes (as no traffic at that hour) - the majority of waiting will be in taxi queue.
You can also try Uber but don't know difference in cost.

Public Transportation is next fastest as NYC Airporter may involve waiting that exceeds the time of you taking AirTrain to JAmaica - > E train towards Manhattan and get off Roosevelt and go upstairs and board Q70. I think your total cost is $7.75 which will take a little less than one hour. You can purchase a MEtroCard when you get to Jamaica plus $1 card fee.