You can have the surgery, go on thyroid hormone medicine, and then prep for RAI when you come home and schedule it for a few weeks after your return.
Thyroid cancer is very slow growing, and the surgery itself usually takes care of the cancer, and the RAI just ensures that all thyroid tissue is destroyed so it won't grow back. My endo. offered me the option of waiting, (I didn't) so I know it's not anything that's dangerous, talk to your doctor about it, and have a great time in Europe!
I would guess you would probably have to wait at least 6 weeks to schedule surgery with someone who is good.
In most cases, there is no rush. I saw my surgeon in mid Sept, had surgery in mid Nov. and RAI in Feb. I didn't want to mess up some plans and the holidays.
My point is, if I were you, I would go to Europe and have the surgery when I got back. This cancer has been growing in you for 10 years or more, so a few months more or less isn't going to make much difference.