First thing is that we are not doctors here, only thyroid patients with lots of experience and knowledge we have learned from our research.
Yes hypothyroidism can cause pregnancy problems if not adequately treated. Just testing for TSH is inadequate to diagnose your thyroid status. You should make sure they always test for both Free T4 and Free T3 every time you go in for tests. A good thyroid doctor will treat a hypothyroid patient clinically by testing and adjusting Free T4 and Free T3 as needed to relieve symptoms, without being constrained by resultant TSH levels. Symptom relief should be all important, not just test results.
We have learned that hypo patients frequently need to have their Free T4 at the middle of the range, at minimum, and Free T3 in the upper part of its range, adjusted as needed to relieve symptoms. Those levels should provide sufficient thyroid hormone to not interfere with becoming pregnant, assuming everything else is good. So you need to get your doctor to agree and keep increasing your thyroid med to achieve those levels, and then re-test every 2-3 months to assure adequacy.
Also hypo patients are frequently too low in the ranges for Vitamin D, B12 and ferritin. You should get those tested and then supplement as needed to optimize. D should be about 50 min. and B12 in the upper end of the range, and ferritin should be about 70 min..