welcome to the forum!
this appears to be normal. you are putting a load on the engine, and the RPM will dip due to load, and the shaking will be because of the RPM dip from the engine. this is a basic 4 cyl engine- so its not as powerful of an engine; expect small vibrations.
P has no load = engine works load free.
R is a load.
N has no load = engine works load free
D has a load.
from p/n into R/d you are going to get a vibration from the engine and a shift inside the tranny from a gear change.
also i want to add. when you are putting a gear into place, it wants to move - but your brakes are holding the car, so its gonna make a slight "jerky" feeling.
i dont know how violent your jerky feeling is, but i do want you to know all cars do this. if its really bad from D straight into R = then you have a problem.