Take a piece of your laminate and lay it upside down next to your door frame, on top of what ever underlay you are using. With a fine tooth saw resting on top of the laminate saw through the door frame. Remove the waste wood and you can then slide your laminate under the gap.
Remember to leave an expansion gap on both sides of the doorway under the frame or your laminate will be likely to rise up in the doorway..
what happens though if you have to start laying the laminate at the opposite end of the room and the laminate runs parallel to the door? i have found that if you slide it under the cut in the door frame you then cannot lift the board to get the angle on it that you need to engage it onto the previous piece.
I use a chisel under the piece I am putting in then press hard on the edge. This creates enough of an angle to allow it to click. A laminate floor fitting kit makes it a lot easier as the tapping block does not dammage the edges.