Whirlwind, I'm so sorry that I can't remember your "real name.
Did he give a reason why it should be done with contrast? Iodine can make MG worse, so if you are not doing well right now you may want to decline his generous offer.
I react to iodine too and have had to premedicate when I did need one (to rule out a pulmonary embolism).
It's your choice whether to have contrast or not. Is the CT itself even necessary? Do you need more radiation in your body? What clinical benefit will you get from having a CT? What clinical benefit will your insurance company get?

Will it really contribute to your quality of life?
I don't do testing anymore unless it is absolutely necessary. Tests don't come without risks. If there is a very good, valid reason for a test, great. If a doctor is running one only because they are "curious," forget it.
I hope you are doing okay.
Annie