Place a piece of laminate flooring face down on top of a small piece of foam underlayment. Set these stacked pieces next to the door jamb in the doorway between the two rooms. Use a dovetail saw to cut the door jambs and casings to size. When you have finished, the laminate flooring and underlayment should slide easily under the door jambs.
Install the laminate flooring and foam underlayment per manufacturer directions in the first room. Once you reach the doorway of the room, cut the laminate flooring so it slides underneath the door jambs and casings. Use a miter or table saw to cut the laminate planks to size through the doorway. Install the flooring in the doorway but stop when you reach the first full row of the next room.
Measure the distance between the last installed row of laminate flooring in the doorway and the wall of the next room. Add ¼ inch to this measurement. The final measurement will be what you need to cut from the first row of flooring in the next room. Mark the measurements on the laminate planks with a pencil. Rip the planks to size on a table saw. Install the planks together as you did in the previous room, leaving a ¼-inch expansion gap between the wall and the planks. When you have installed the entire first row, the row should match up with the laminate flooring in the doorway.
Install the rest of the laminate flooring in the second room per manufacturer directions.