Hello Maggiebee,
You definately want to get your daughter tested for Thalassemia. It is always the best option.
And remember, Thal(Minor) is NOT a major problem. As Andy would say - It is a good idea to give her Folic Acid if she is a Thal(Minor).
As Sally mentioned, if we know she is Thal(Minor), that information can be helpful in avoiding Iron Supplements(which might NOT be helpful to her)
Thal(Minor)'s live a very normal life and most of Thal(Minor) - do NOT know they are Thal(Minor)'s until they either get themselves tested for Thalassemia or the hard way(their child is diagonised with the severe form - Thal(Major)) and the reality is thousands of parents learn it the hard way.
There are an estimated 80 to 90 million Beta Thalassemia(Carriers) and around 26 million Alpha Thalassemia(Carriers). There are a lot more who are NOT diagonised.
Hemoglobin Electrophoresis is helpful in diagonising Thalassemia. Also, it would be helpful to know if she if she at all is Thal(Minor) - if she is Alpha Thal(Minor) or Beta Thal(Minor).
Do ask questions and learn as much as you can.
-Narendra