Do you want to purify it for preparative purposes or for analytical purposes? If it is only for analytical purposes then consider using electrospray mass spectrometry. Hemoglobins are easy to detect by electrospray mass spectrometry, and with a little more effort you can quantify them by mass spectrometry.
Another question, if you are looking for concentrations, are you looking for the intact Hb A, or is it sufficient to determine beta hemoglobin concentration? If you are using mass spectrometry it is easier to analyze for beta hemoglobin than to analyse for the tetramer. Also, just to be clear, I assume you are looking for Hb A and not Ab A2. Is that right?
Another question: what is your matrix? Is it whole blood or something else, such as packed red cells or a crude hemoglobin extract?