Kepler is a simplify model to understand the motion of planets. If you want to know the detail of the trajectory,
yes. you need Newton's law.
You can check out [url=http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=547.msg1808#msg1808]motion of Moon, Earth relative to the Sun[/url], which simulate gravitation forces between 3 objects. If you have more planets, it can be done with simulation easily. But you will have to set up the right initial conditions, otherwise, the system might not form a solar system if the total energy is not in the correct range.