looks like there is availability on both flights out of JFK on 14th, morning and also evening, and also on connecting flights on 15th.
assuming u already registered as QRPC member u should be able to transfer your AMEX rewards points to QRPC. did this in the past. its at a rate of 5:4 and goes rather quick as i remember. but im based in europe, may be different for US customers?
but in any case i would call qatar first to check for availability before transferring any miles!!!!
u can check for availability yourself by loggin into QRPC and try to book with miles. when there is regular availability (not the green flagged Q2 Flexi awards) there should be availability! but again, call qatar to verify before transferring any miles or book any flight!