Desmopressin is a synthetic agonist of Vasopressin which acts on V1 receptors on the renal collecting duct to decreased the volume of urine and also decrease thirst by inducing hyponatremia. After consulting lists of drugs not to be used by people with LQTS I did not find either vasopressin or desmopressin, so I am assuming it is acceptable to use this drug. However, the benefit of th drug is likely not to be very significant, and in studies the improvement in bed wetting was minimal.
I don't know several things about your son: first does he have defibrilator and second what subtype of LQTS does he have. Depending in the answers to these questions he may be protected from VT/VF and use of the medication may be acceptable. But I would say that since the benefit from it is so small from the medication that I would advise you not to take it.