i'm not sure what test(s) they will do.
I want to stress to you that most doctors are satisfied that one test - the TSH - will tell them everything they need to know. It is NOT. The TSH can take years to elevate above the normal lab range when actual thyroid hormones are low, and you're doomed to suffer a long time until that happens. Sometimes it never elevates. You can see the problem with testing only TSH.
Be polite about it, but be insistent
on the tests I named above. If insurance and cost containment is an issue, at the very least
have TSH, free T4, and antibodies. The postpartum period is a common time for autoimmune thyroid trouble to set in, and the antibodies will show it even if the other levels look ok.