When your doctor says he'll "burn" your thyroid, what he means is that he'd recommend RAI (radioactive iodine). You are given a dose of radioactive iodine, and over the course of several months, your thyroid gland is destroyed by the radiation. Once it is destroyed, you will be hypOthyroid and will have to be on replacement hormones for the rest of your life. RAI is seldom, if ever, done on pregnant women.
So, to answer your question, many women who are hypo and on meds have successful pregnancies. However, it is very important to have your condition stabilized with drugs before getting pregnant and throughout your pregnancy. Fetal development can be impacted by maternal thyroid hormones.
If you decide on RAI, it would probably be best to wait long enough after for your condition to re-stabilize before getting pregnant...that can be up to a year or more.
Read all you can about RAI. It is a permanent fix for hyper, but realize you will be hypo for the rest of your life afterwards. Make sure your doctor answers all your questions and you really understand everything.
Have you ever been tested for or told you have Graves' disease? Graves' is autoimmune hyperthyroidism...your immune system sees your thyroid as foreign protein and sends out antibodies to destroy it. The test for Graves' is TSI (thyroid stimulating immunoglobulin). If you haven't had this test, you should. Graves' can go into remission (symptoms go away), but you always have it and it can flare up at any time. If you have Graves', it's probably something you want to know before getting pregnant.
Good luck with it all.