Your mother's brother's daughter is your first cousin. The marriages taking place within the family is an age-old tradition. However, it comes with certain health-related risks. According to the study the children who are born by marriage between first cousins are at double risk of suffering from birth defects. Congenital abnormalities in kids will be common.
Usually, the risk of suffering from birth defects is low if the parents are not blood relatives. The same risk doubles when the parents marry within the family. Birth defects involving nervous system, lungs and cardiovascular system commonly take place and sometimes it can even lead to death. Kids are at high risk of suffering from Down's syndrome.
You and the girl share a common grandparent. It is a very common fact that both the boy and girl might inherit a recessive gene that is faulty. In such cases, the child is at high risk. When the marriage takes place outside the family, the risk decreases to a great extent. Those who share common ancestors are at high risk of carrying faulty recessive genes. If they marry and give birth to kids then such kids are at high risk of suffering from genetic disorders.
I would suggest that you and your cousin go for genetic screening before getting married. It may not be possible to identify faulty recessive genes that you two inherit but still, the problem can be solved to a great extent. Specialists record the health history of the family to know the health disorders that family has suffered from in the past. Cystic fibrosis screening, carrier screening is carried out. Haemoglobinopathy which includes recessive conditions such as sickle cell disease and beta-thalassemia is carried out. Level of haemoglobin detects the carriers.
In short, since you are about to marry the girl with whom you share a close biological relationship, your kid is at high risk of suffering from the genetic disorder as both of you share the genes in greater proportion.