I have never heard of a homeopathic remedy curing Graves’ – if yours works I’d be really interested to hear about it.
Just a little word of caution: If your bloodwork shows you to be hyper, even though you don’t have any visible symptoms, hyperthyroidism can cause osteoporosis. This thinning of your bones doesn’t happen all at once, of course, but over time they will lose more and more mass. You might want to consider talking to your doctor about having a bone scan from time to time, and in the meantime to take calcium tablets.
Also make sure your doc keeps an eye on your heart – untreated hyperthyroidism can cause heart problems, though I don’t know if you have a racing heartbeat or palpitations.
I think you’re wise to put off RAI for a while to see if you go into remission, especially as you are coping well and have no symptoms. You could always have the RAI at a later date if it worsens and you find the different medications available don’t work and you’re feeling ill.