Your wife needs to be put on thyroid replacement hormone. Normal dose to start with would be levothyroxine at 25 mcg. Target TSh will be about 1.0.
Her levels should be tested monthly thoughout the pregnancy and her meds increased as necessary to keep TSH as close to target as possible. FT3 and FT4 should also be tested and meds adjusted to keep them in the upper half of the reference range.
TSH of 6 is not terrible and am sure that your wife and baby are ok, but treatment is required for the rest of the pregnancy to give best possible outcome.
If any doctors says not to treat based on TSH of 6 they are dead wrong and you need a second or even third opinion..
Relax I am sure the baby is fine and your wife will be fine but she does need to take her thyroid health seriously especially during pregnancy not only is her body dependant upon it the baby is also leaving it untreated could cause a number of problems but she is early enough she can fix it and everything will be fine.
She needs to be seen by a good endocrinologist and be monitored and treated through out the pregnancy and after. After is also very important because hypothyroid can lead to postpartum depression.
If you would like to learn more on what this cause if left untreated just search aroung the internet and will see the negative effects it can have on the baby.
And just a note to help you feel better my 2nd child was born while I was untreated with hypothyroid and luckily she is fine but if I had known I had a problem and knowing what I know now I would have demanded treatment. My first on the other hand was born while I was hyper and has craniosynostosis as a result. Thyroid is very very important during pregnancy don't let any doctor tell you otherwise.