Another thought is to go ahead and ask the doctor about retesting in 4 weeks, even though you can't get an appointment until much later. I can't see why the doctor would object since you can't get an earlier appointment. If the answer is no, there are surely other places that will at least do the testing for you anyway, so that you can assess your thyroid hormone levels. If you do that, be sure to request the actual, biologically active thyroid hormones, FT3 and FT4 (not total T3 and total T4), along with TSH..
After seeing your post I did some quick searching and found an article that might be of interest to you on this subject. Here is the link.
http://www.ithyroid.com/graves_treatments.htm
I found this paragraph especially interesting.
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Methimazole with its longer half life of 4-6 hours can be taken once daily. The starting dose is 20 to 30 mg. Patients on either ATD usually have a dosage change after 4-12 weeks. Methimazole causes euthyroidism quicker, taking four weeks, while PTU may take as long as 12 weeks. If there is no improvement, the dose is increased. With evidence that the drug is working (weight gain, reduction in goiter), the dosage is usually reduced.
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Understand that I have not had Grave's, so I have no personal experience with this, but it doesn't sound like you should be concerned with the prescribed dosage. Hopefully some of our members with direct experience will also respond.