In pregnancy, which is the best parameter to be measured in thyroid function test?
Ref. The Short Textbook of Pediatrics. Pg 72
 
Fetal thyroid starts functioning after 12 weeks. Till then the fetus is entirely dependent upon the maternal supply of T4 through the placenta, for all neurologic developments .

TRH crosses the placenta but TSH crosses it very minimally.
Maternal total T3 and T4 are increased by 18 weeks but free T4  and T3 levels are unchanged .Maternal TSH levels remains normal.
Secretion of T4 and T3 is 20: 1.

However women with high risk factors should have their serum TSH level checked in their first antenatal visit
TSH
Free t3
T4
Total t3