The probable reason you have not been asked to monitor your glucose more often is because at this point you have not been put on medication of any sort. So any glucose changes will happen fairly slowly as your system adjusts to the low-carb lifestyle. Since you cannot take medication if you see a high number, it is almost pointless to do the glucose test. And since you are not taking medication at this point, lows are not an issue.
So since you cannot do anything about any errant numbers if you DO test, testing often is not something that will help you at this point. So you need to strictly adhere to the diet and give your body time to adapt to it. Your doctor can see from the blood test results when you return whether the diet change has brought your overall glucose levels down within normal ranges. I hope so, for then all you would need to do is to continue the new lower-carb diet and exercise in order to maintain your health. If you ARE put on medications of any sort, he will probably start having you test more often at home to make sure the dosage is correct. So I would encourage you to just take it one step at a time and make those diet and exercise changes for now.
Your doctor's advice is surprising to me, also. I'm guessing that s/he is not a diabetes specialist and that's the type of physician who should be guiding your diabetes care. Specialists might be called endocrinologist or diabetologist.
None of us here is a physician, but we're long-time diabetics or care-givers for diabetic children.
You didn't mention if you've been diagnosed with Type 1 or Type 2, and the treatment options vary for these types.
Your instincts are good, Candikane. Whether you're Type 1 or 2, monitoring your BG (blood glucose) and learning how your BG responds to food, exercise, stress, etc. is very important.