I've beta thalassemia minor and my husband have e trait. Is it necessary to test our baby? Is there any chances to get disease of our baby?

Not likely. Unless your infant is showing signs of anemia, you may do an hemoglobin electrophoresis at any time after several months of life. Fetal hemoglobin (normal) is usually present in decreasing amounts until around 18 months. Once the electrophoresis is done, you will know your baby's hemoglobin type. Discuss with your doctor.
Test yes . You need to discuss this with your physician. You need to test but i'm not certain when the best time is. You will never be comfortable until you know.