Wirelessly posted (BlackBerry: BlackBerry8530/5.0.0.1030 Profile/MIDP-2.1 Configuration/CLDC-1.1 VendorID/417)
Unless the OP will have checked baggage, this transfer should be quite doable via rail -- as long as the DFW-EWR flight arrives on or close to schedule. (If the DFW-EWR flight takes a delay before boarding at DFW, AA should re-route the OP out of DFW.)
If the OP is going to make the transfer by rail, he should familiarize himself with the process before arriving at EWR. He will want to buy his EWR-NYP (New York Penn Station) tickets at the NJ Transit vending machine near the AirTrain station at his EWR arrival terminal. At NYP, he will head over to the Long Island Rail Road section of the station. I believe that the LIRR vending machines still sell a combo ticket that includes that LIRR portion from NYP to Jamaica, and a $5 Metrocard on the same ticket to cover the cost of JFK AirTrain from Jamaica to the OP's departure terminal (T7 if on BA metal; T8 if on AA metal). If such a combo ticket is purchased, the OP should be sure to get the ticket back from the LIRR train conductor after the ticket is punched.
LIRR departures from NYP to Jamaica after 4:09 PM will require purchase of a "peak" fare ticket.
If the OP is at least 62 years old, discounted fares are available on NJ Transit; on the LIRR, the minimum age for the senior discount is 65.