HI Mahbub,
The reports indicate that the child has HbE beta thalassemia, which means she has a beta thal gene and an HbE gene. The almost complete lack of HbA shows that this is HbE beta zero. This is shown by the electrophoresis, with HbE at 30% and the HbF at over 60%. Right now her Hb level is high enough where transfusions are not necessary. The long term is not easily predictable, as the production of HbF can be affected by the presence of other modifying genes, like alpha thalassemia deletions and the Xmn I(+) polymorphism. DNA testing can tell you if any of these modifier genes may be present.
Currently her Hb is in the range of thal minor. This may progress to an intermedia or possibly even major status as time goes by, depending largely on the presence of any modifiers that may result in a higher level of HbF. It is possible that transfusions will eventually become necessary. If the DNA testing can be done to look for other genetic modifiers, you will get a better picture of what to expect. Right now, she's doing good, but you've seen that her immune system may not be as strong as it should be. Special attention should be made to nutrition and eating habits, and precautions should be taken to minimize spread of infections to the child. She should learn to wash hands often, especially when touching things others have touched.
Time will tell. Some patients do fine but eventually need to transfuse as adults, while some have to begin transfusing as children. Enjoy her birthday and think about having the DNA tests done to check for modifying genes.