Beta Thal Minor, Doc wants to give Iron infusion

Wife has Ferretine level of 13 ug/l  (normal range 10-220 apparently)
Hemoglobin reading 10. Very low apparently according to Doc. Doc says that she is surprised that my wife does not faint. Wife is actually a hardcore fitness teacher and feels ok right now. The test was part of general yearly female checkup.

Doc wants to give her small dose of iron infusion spread out into 2 doses over 2 week period. Wife said she is Beta Thal Minor and that apparently she should not be taking it. Doc says that she is fully aware but she actually needs it and she should take it  

Me (husband), don't know what to do? Let her go ahead with it or ask her to cancel the appointment?

I find this all so confusing even after many years of trying to understand it!!!!!
Oh also got these two readings-

TSH Basal 1.80mU/l
B12- 643 pmol/l

Ok as we need to decide fast (it is tomorrow). We decided that she will get the first dose of 200mg and cancel the second one of 300mg. The doc had said it was very low dose and won't affect her organs  

Either way as my wife feels normal so we don't want to risk by taking the second infusion. I already feel conflicted about the first 200mg infusion.

Please any advice?

I'm sorry I didn't see this earlier. Been occupied with my own wife's health.

A full iron panel should be done to diagnose iron deficiency in thal minors. Ferritin, alone is not sufficient and the Hb level will be lowered by thal minor, so not much can be told when the Hb is in a normal range for a thal minor. If the serum iron and TIBC are not within a normal range, iron should be tried. If a trial does not raise her Hb, iron probably isn't going to help and long term, it can cause harm. Don't stress if she does go through a short iron trial. It won't harm her and will give a better indication if iron is part of her anemia. Ifit isn't, folate and B-12 are far more likely to be helpful than iron is in thal minors.

And the two results you left at the bottom of the post.
TSH is a thyroid test and her level is normal.
Her B-12 is solid. It would not hurt her if it was raised higher. It's one of the things many thal minors mention as helping their Hb level.