Haemoglobin less then 12 gm percent is always suggested for other investigations. Well 7.2 gm percent might be unlikely just due to iron deficiency alone. There might be other corelated conditions which might be causing this. Like lets say irregular menstruation periods, heavy menstruation, frequent abortion, blood loss from gastro-intestinal tract or presence of any chronic disease which may show signs and symptoms you can notice like dark urine,blood in stool,on/off fever and so so..
I don't think its a good idea just to depend on prescription iron suppliments, as it might not help. So the first thing you need to do is all investigations of blood including platelets,abdomen scan,thyroid function tests,urine and stool check, bone marrow and so so...,This way we could know what is the cause behind the low haemoglobin and treat accordingly. Just taking iron suppliments and diets may temporary relief without curing the actual cause. So don't just neglect, if needed change your doctor.
As far as your concern about heart risk, this might not itself cause any heart disease but it will sure increase the heart load,which sometimes can cause heart failure like symptoms. When you have such low haemoglobin any kind of co-existing disease may have a major complications. So don't delay, just do all the examinations and find out what is the real cause behind low haemoglobin.
If you have anything to ask feel comfortable...