Yes, paying the dealer whatever it takes to fix it is always a great option.
I am assuming that you did not post here just to have that confirmed... But
if you want the people on this group to help you diagnose your problem,
please tell them as much as you know -- they can't see, hear or drive your
truck (or is it even a truck?): vehicle type, engine type, year, mileage,
any idling and driveability problems, some maintenance history perhaps. Does
it shake just at idle or under other conditions as well?
The fact that the MIL ('check engine light') is on may or may not be related
to your shaking. But it needs to be addressed first. There are trouble codes
stored in the computer. Have them read (Autozone presumably does this for
free) and post them here with the rest of the information.