In my view it is unlikely that half of a thyroid gland could produce the amount of thyroid hormone needed by a patient. So, if she has not been tested for the biologically active thyroid hormones, Free T4 and Free T3 (not the same as Total T4 and Total T3), then she should get those done. If those are below the middle of the range, and she has symptoms that can be related to being hypothyroid, then that would be a good indicator that she is hypo and needs to be on thyroid med. In addition I highly recommend testing for Vitamin D and ferritin. Both are important for her.
Does she have any other symptoms?
I see that you are in Australia so you will be subject to the rules of the national health system there. Typically there is the belief that only TSH testing is necessary to diagnose and treat a hypothyroid patient. That is very wrong, so you should insist on testing her for Free T4 and Free T3. If you are able to get that done, then post results and reference ranges shown on the lab report and we will be happy to help interpret and advise further.