Lots of good info here already.
EWR > NYC Penn Station is 25 minutes on NJ Transit. Of course that doesn't include the Air Train from the Terminal to the EWR train station, the walking, the wait time, etc. But an hour for all of it is reasonable.
The LIRR to JFK leaves from NYC Penn Station, so that's a plus for you. You will take the LIRR to Jamaica Station (22 mins), then the Air Train to your terminal (another 15-25 minutes, depending on which terminal). Then you'll have to walk your bags another 10 minutes to the actual terminal. Welcome to NYC. There's no organization or efficiency here.
This can be done in two hours, but it's tight. You won't have to wait long for the EWR > NYC Penn Station trains since it's rush hour. LIRR trains to Jamaica Station depart every few minutes.
The real problem is NYC Penn Station. Even for locals is so inefficient and terribly organized that it gets complicated to navigate. Be prepared to carry bags up stairs. Then you have to find the LIRR side of the station. Then buy a ticket (or you can purchase this on the train for a $5 or so surcharge). Then figure out which track you're train is leaving from. They really couldn't have made it any more complicated, so don't hesitate to ask people for directions/help, and you'll probably have to ask more than one.
Hope it works out.