Most likely this developed post-partum and was not going on during the pregnancy -- usually TSH is checked during pregnancy.
Post-partum there are two primary possibilities: 1) Post-partum thyroiditis which often gives a transient hyperthyroidism (not always present) then a hypothyroidism which resolves in a few months in most cases or 2) Hashimotos which is an auto-immune attack on the thyroid causing destruction and is more likely to be long-term.
At 8 months would gamble on hashimotos -- ask them to check the antibodies against the thyroid.
The treatment is correct - check a TSH about 6 weeks later and further adjust the synthroid to get the TSH to about 1.0.
Nursing should not be effected by the treatment and the baby should not be at risk by nursing.
This may make you feel better--looking back, I'm pretty sure I was getting hypo while pregnant with my second child, and definitely was while pregnant with my third. I also nursed both while probably very hypo. And there appears to have been NO harmful side effects to either. They have high IQ's and have done REAL well in school. Whew. I, too, was put on a med like Synthroid, and 75 mcg. sounds familiar. I eventually made my way up to .125. But I do want to tell you that being on Synthroid never, ever rid me totally of symptoms, no matter how low I got my TSH. It was switching to Armour, which is pig thyoid and gives you not just T4 but T3, T2, T1 and calcitonin, which really stopped all my symptoms. Just something to tuck away in the back of your mind. And perhaps your child will be just fine as mine were and are! :o)