This woman is suffering from hyperthyroidism so I would go for Radioactive iodine (RAI) therapy. Lets discuss the options one by one:-
Surgery
Surgery (to remove the whole thyroid or a part of it) is not extensively used now a days, was once a common form of treatment for hyperthyroidism instead hyperthyroidism are quite effectively treated by the radioactive iodine method.
The goal of the surger is to remove the thyroid tissue that was producing the excessive thyroid hormone. However, if too much tissue is removed, an inadequate production of thyroid hormone (hypothyroidism) may result. In this case, thyroid replacement therapy is begun. The major complication of surgery is disruption of the surrounding tissue, including the nerves supplying the vocal cords and the four tiny glands in the neck that regulate calcium levels in the body (the parathyroid glands). Accidental removal of these glands may result in low calcium levels and require calcium replacement therapy.
However, some Graves' disease patients who cannot tolerate medicines for one reason or another or patients who refuse radioiodine opt for surgical intervention. Also, some surgeons believe that radioiodine treatment is unsafe in patients with unusually large gland, or those whose eyes have begun to bulge from their sockets, claiming that the massive dose of iodine needed will only exacerbate the patient's symptoms. The procedure is quite safe - some surgeons are even treating partial thyroidectomy on an out-patient basis.
Propanolol
One of the main classes of drugs used to treat these symptoms is the beta-blockers. These medications counteract the effect of thyroid hormone to increase metabolism, but they do not alter the levels of thyroid hormones in the blood.
Iodinated contrast agents
In severe thyrotoxicosis from Graves disease or subacute thyroiditis, iodine or iodinated contrast agents have been administered to block T4 conversion to T3 and the release of thyroid hormone from the gland. This therapy is reserved for severe thyrotoxicosis because its use prevents definitive therapy of Graves thyrotoxicosis with radioactive iodine for many weeks. Either a saturated solution of potassium iodide (SSKI) at 10 gtt twice daily or iopanoic acid/ipodate (1 g/d) can be administered with rapid reduction in T3 levels. Take care to not administer these drugs to patients with toxic multinodular goiter or toxic adenomas. The autonomous nature of these conditions can lead to worsening of the thyrotoxicosis in the presence of pharmacological levels of iodide, a substrate in thyroid hormone synthesis.
Propylthiouracil (PTU)
There are 2 main antithyroid drugs available for use commonly are methimazole (Tapazole) and propylthiouracil ( PTU). These drugs accumulate in the thyroid tissue and block production of thyroid hormones. PTU also blocks the conversion of T4 hormone to the more metabolically active T3 hormone. The major risk of these medications is occasional suppression of production of white blood cells by the bone marrow (agranulocytosis). (White cells are needed to fight infection.) It is impossible to tell if and when this side effect is going to occur, so regular determination of white blood cells in the blood are not useful.
So left alone is
Radioactive iodine (RAI) therapy
In Radioiodine (treatment) therapy, Radioactive iodine is given orally (either by pill or liquid) on a one-time basis to ablate a hyperactive gland. The iodine given for ablative treatment is different from the iodine used in a scan. (For treatment, the isotope iodine 131 is used, while for a routine scan, iodine 123 is used.) Radioactive iodine is given after a routine iodine scan, and uptake of the iodine is determined to confirm hyperthyroidism. The radioactive iodine is picked up by the active cells in the thyroid and destroys them. Since iodine is only picked up by thyroid cells, the destruction is local, and there are no widespread side effects with this therapy. Radioactive iodine ablation has been safely used for over 50 years, and the only major reasons for not using it are pregnancy and breast-feeding
(This woman's pregnancy test is negative). This form of therapy is the treatment of choice for recurring Graves' disease, patients with severe cardiac involvement, those with multinodular goiter or toxic adenomas, and patients who cannot tolerate antithyroid drugs. Radioactive iodine must be used with caution in patients with Graves' related eye disease since recent studies have shown that the eye disease may worsen after therapy. If a woman chooses to become pregnant after ablation, it is recommended she wait 8-12 months after treatment before conceiving.
Often, due to the difficulty of picking the correct dose, the treatment results in an opposite condition - hypothyroidism. However, that is usually easily treated by the administration of levothyroxine, which is a pure synthetic form of T4.

Lets see the correct answer and explation by Hero.