Cousins are not included from those who are forbidden to marry so yes this is permissible. Allah says in Surah'tul Nisa
23. Forbidden to you (for marriage) are: your mothers, your daughters, your sisters, your father's sisters, your mother's sisters, your brother's daughters, your sister's daughters, your foster mother who gave you suck, your foster milk suckling sisters, your wives' mothers, your step daughters under your guardianship, born of your wives to whom you have gone in - but there is no sin on you if you have not gone in them (to marry their daughters), - the wives of your sons who (spring) from your own loins, and two sisters in wedlock at the same time, except for what has already passed; verily, Allâh is Oft*Forgiving, Most Merciful.
As for the issue of genetics then it has more to do with simply having a defect in your genes than marrying one's cousin. If there is a defect in the family genes then yes its not advisable to marry one's cousin due to the possibility of having those very genes in both the mother and father thus resulting in a mental or physical handicap in the baby. This happened to my aunt and uncle who are cousins and all of their children were severely retarded.
...may Allah grant my wish...Amin