HI Christine,
I think you may need a prescription for low iron formula in the US. I wouldn't say at this point that iron will harm Lauryn, although at this age it isn't really needed. The problem with iron is that it will add to the overall iron levels and when transfusions to begin, it will mean an even earier start to chelation, which is best put off as logn as possible.
The only references I can find online about iron in infants with thalassemia is that normally low iron formula is prescribed. I can't find a single reference that says that thal babies should take iron fortified formula. If a doctor tells you to give high iron formula, ask why it's necessary during the first few months, especially considering it will add to iron problems later on when transfusion begins.
How have her hemoglobin readings been? She is growing well, which is a very good sign.