All LIRR trains out of Penn Sta except the Port Washington line stop at Jamaica. Just look at the departure board for the track number of the next train to Jamaica. Some go express to Jamaica while others stop in Woodside / Forest Hills / Kew Gardens, so you could shave a few minutes off your trip by timing the connection to meet the next express.

At that hour I think your biggest hold up will be the lines at the LIRR ticket machines and booths. I'd recommend buying your ticket in advance, if you can, or just getting on the train and paying the small penalty for buying your ticket on board.