S.,
I was diagnosed with Graves disease back in 2000 (when I was 29). I did the radioactive iodine and had no trouble at all--no side effects, and it worked well. My gyne suggested waiting to attempt conception for a year though, instead of 6 months "just to be sure". I got married about 6 months after the iodine treatment and we were eager to start a family...so that extra 6 months was hard...but I got pregnant the first time we tried. That one did end in an early miscarriage, but I have another autoimmune condition that was probably more to blame (plus I had a lot of other stress going on at the time) I have since gotten pregnant two additional times--both on the first cycle we attempted--and have two beautiful and healthy boys.
I also happen to be a nurse in an OB-Gyn office and when a patient calls me with these questions, I tell her this. When you hear about trouble conceiving or recurrent pregnancy loss with Graves Disease, it is likely referring to untreated Graves. When the Graves is active and untreated, everything is running on "hyper mode"; some women's periods get irregular or they don't ovulate when that happens--that is where the trouble begins. Similarly, when pregnant, the hyperthyroid state in untreated Graves may trigger pregnancy loss--maybe due to the "hyper" metabolism of everything in your system, or maybe due to the autoimmune component of the disease. Besides, if miscarriages occur after the Graves is in remission, there are a few medications that can be taken during pregnancy that really decrease the chance of it happening again.
Incidentally, the practice I work for has had several cases of women who got pregnant and we diagnosed their Graves through a routine early pregnancy thyroid screening test. So there are women who indeed get pregnant with no trouble even with active Graves. (Those moms are started on the pill treatment so their Graves doesn't go out of control while pregnant--and every one of those babies has been fine too, even when mom is on the anti-thyroid pills.)
My advice is to get treatment. Your future fertility should be just fine. (I initially tried pills to treat mine but that only kept it shut down for about a year. The RAI worked...I am now on daily thyroid medicine for the underactive state you go into when the Graves is stopped and get my level checked yearly.)
Again, I had no ill effects from the RAI and have had no trouble getting pregnant over the past 6 years. My boys are just fine.
Good luck and let me know if you have any more questions.
C.